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After the recent Notre-Dame de Paris fire, there has been a heavily re-posted tweet going around in response to an earlier claim that a golden cross did not melt or deform - due to an act of God.

the Notre Dame Cathedral was a wood fire, and as such could only have reached 600°C, while gold requires 1064°C to melt.

The melting point of gold varies based on purity, and can thus be lower than 1064°C.

However; do wooden buildings, such as the Notre Dame Cathedral, burn at temperatures above 600°C?

I'm obviously not interested in any debate over whether this was an "Act of God" or other unprovable matters.

In terms of personal research, what I have found is that while wood itself will not burn much hotter than 600°C, once it turns to charcoal - it can then reach over 1100°C. However I don't know enough about physics/chemistry or fires, to make a reasonable judgement on how that applies in a real-life fire.

Probably yes: According to at least one expert, the temperature in the Notre Dame fire must have been extremely high, and probably exceeded 600°C.

Yesterday the Süddeutsche Zeitung, one of Germany's most reputable newspapers, published an interview with the director of the German Technisches Hilfswerk (the Federal Agency for Technical Relief) and former director of the Fire Departments of Berlin, Albrecht Broemme. The interview covers several aspects of the Notre Dame fire (for example, Broemme explains why using water bombers was out of the question). He also discusses why this was an extraordinarily difficult task for the fire fighters. One reason he mentions is the extreme heat of the flames:

Der Farbe der Flammen nach zu urteilen müssen die Temperaturen bei 800, 900 Grad gelegen haben.

(My translation: "Judging from the color of the flames, temperatures must have been 800 or 900°C.")

Of course, this interview is not a peer-reviewed publication on the temperatures that wood fires can reach. However, based on this expert statement, there is little reason to doubt that a fire such as the Notre Dame fire can be far hotter than the 600°C the Twitter comment mentions. Note of course that his statement does not answer whether the fire was really hot enough to melt the golden altar cross, or whether the choir was actually exposed to this extreme temperature.

Without acknowledging any of the conditions actually present in the church, wood fires can get much hotter than 600°C.

The maximum temperatures measured within the pile were of the order of 800, 1000, and 1200 °C for piles composed of 1.27, 2.54, and 9.15 cm sticks respectively, although the maximum temperatures for a given size stick appeared, from all data obtained, to be somewhat dependent upon the structure of the pile. The prescribed temperature-time curve of a standard fire exposure test 1 is also shown in figure 4 from which a general agreement may be noted.
_{D Gross: "Experiments on the Burning of Cross Piles of Wood", Journal of Research of the National Bureau of Standards- C. Engineering and Instrumentation Vol. 66C, No.2, April-June 1962. (PDF)}

A nice pile of wood with good ventilation can get apparently really hot:

Fire plume temperature data suggest a maximum turbulent flame temperature in fully developed compartment fires of about 1500 C for stoichiometric and adiabatic conditions. Experimental results for crib and pool fires are presented to support the trends indicated by the approximate analyses.

In general, from equations 12 and 13 for stoichiometric conditions, the temperature is given as

[MATH FORMULA]

where Tf,ad is the stoichiometric adiabatic flame temperature. Recorded gas temperatures near the ceiling are reported as high as 1350 C [21], and mean temperatures over the peak burning period are 1000 to 1200 C for polyethylene fires [21] and approximately 900 to 1200 C for wood cribs [20]. For turbulent fire plumes, having a radiative loss fraction Xr, a similar formula applies to the combustion region. This turbulent flame (centerline) temperature is given as [18]

[MATH FORMULA]

From the best available data [22–24], the turbulent mixing parameter, kT, is found to be approximately 0.5 for cp 1 kJ/kg K. As the fire diameter increases, the radiative fraction falls due to soot blockage [25]. Fig. 4 shows flame temperature data for turbulent plumes as a function of Xr. The extrapolated adiabatic temperature is approximately 1500 C. For a realistic adiabatic flame temperature of 2000 C, the actual turbulent mixing factor is approximately 0.75 or a turbulent dilution factor of 1.5. For a large fire in a compartment with large vents, the core maximum flame temperature should approach the turbulent adiabatic flame temperature.
_{James G. Quintiere: "Fire Behavior in Building Compartments", Proceedings of the Combustion Institute, Volume 29, 2002/pp. 181–193. DOI}

But to be very sticklish, the claim is actually somewhat correct. Why?

_{M. J. Spearpoint And J. G. Quintiere: "Predicting the Burning of Wood Using an Integral Model", Combustion And Flame, 123:308–324 (2000). DOI}

Or to put it simply:

A bonfire can reach temperatures as hot as 1,100 degrees Celsius (2,012 degrees Fahrenheit), which is hot enough to melt some metals.

Most types of wood will start combusting at about 300 degrees Celsius. The gases burn and increase the temperature of the wood to about 600 degrees Celsius (1,112 degrees Fahrenheit). When the wood has released all its gases, it leaves charcoal and ashes. Charcoal burns at temperatures exceeding 1,100 degrees Celsius (2,012 degrees Fahrenheit).

Gabriella Munoz: "How Hot Is a Bonfire?", Sciencing, April 26, 2018.

Wikpedia says

This is a rough guide to flame temperatures for various common substances (in 20 °C air at 1 atm. pressure):

Wood 1,027 °C (1880.6 °F)
Methanol 1,200 °C (2192 °F)
Charcoal (forced draft) 1,390 °C (2534 °F)

and gives for adiabatic flame temperature maximum even:

Wood Air 1980°C 3596°F

The French authorities seem to have suggested that inside the church 800°C might have been reached:

Contrairement aux pompiers américains, les sapeurs-pompiers français s’attaquent aux incendies par l’intérieur et non de l’extérieur. Cette tactique est plus dangereuse pour les hommes mais plus efficace pour sauver le patrimoine, observe l’expert Serge Delhaye. Si l’on se concentre sur l’extérieur, on prend le risque de repousser les flammes et les gaz chauds, qui peuvent atteindre 800 degrés, vers l’intérieur et accroître les dégâts. »
"Six questions sur l’incendie de Notre-Dame de Paris", Le Parisien, Jean-Michel Décugis, Vincent Gautronneau et Jérémie Pham-Lê| 15 avril 2019, 23h40

Most sources seem to quote a temperature of 1000°C for this incidence, but other sources even go up to 1400°C:

Fires peak at 1,400°C, explains professor Guillermo Rein, the head of Imperial College London's fire-studying Hazelab.

Nicole Kobie: "The hot, dangerous physics of fighting the Notre Dame fire", Wire, Tuesday 16 April 2019

Wood is a perfectly acceptable and common material used in metal forging even more so when it becomes partially combusted (charcoal). What really determines the heat though, is the amount of oxygen it can get. If there were medium-high winds blowing on the building it could have melted even steel beams.

Reference: https://youtu.be/x_wYozMBWNk

In that video you see a forge burning raw wood getting hot enough to make steel white which typically happens around 1200C (reference2: http://www.smex.net.au/reference/SteelColours02.php)