EXPERT SAYS; PRESSURE RISE IS RED HERRING

(Pressure*Volume)/Temperature is a constant.

In the well the volume can't change when the cap is on except for leaks. So if the pressure goes up then the temperature must go up also to preserve the ratio.

This same equation applies to Chinook winds that blow down the east side of the rocky mountians. The volume of the air in the wind can't change because the atmosphere is holding it down. But as the wind loses altitude is must gain pressure and consequently the air heats up. Ask anyone from Colorado Springs or Denver.

But back to the well. The argument is a chicken/egg thing. If the pressure is rising because the oil is backing up in the pipe then the temperature will be forced to go up. If the oil is getting heated somehow then the pressure will go up.

BUT IN ANY CASE THE TEMPERATURE WILL GO UP. If the pressure gets very high then the temperature will go up to very high temperatures. I like doom but I don't think the oil or methane will reach ignition temperature. If they are using a rubber gasket to form a seal on the top cap it might melt or some other problem will happen first.

[link to easycalculation.com]

The equation I quoted in my first reply is called the combined gas law which combines Charles's law, Boyle's law, and Gay-Lussac's law.

How hot will it get?

One problem is that the hot pipe might effect the stability of the mud section of the ocean floor which will stress the riser pipe with the huge weight of the BOP and cap. It might bend and break.