Conditions at the bottom of a VERY deep hole
If it is enclosed and undisturbed there would be a risk of the heavier gasses collecting at the base of the hole, with carbon dioxide, argon, neon and xenon displacing the nitrogen and oxygen. Hence the danger of asphyxiation for any organism at that depth. Mixing, to keep the air homogeneous would also have the effect of heat transfer to further up the hole, so you will need artificial mixing and cooling. There are likely to be traces of helium and hydrogen at such depth, but not enough for the upward flow of such light gasses to have any significant mixing effect. However, hydrogen will be a potentially explosive problem at the enclosed surface environment. At these temperatures water rock reaction at the exposed base of the hole would be rapid. It is not clear whether your hole would have punched through to the mantle. I'm assuming it would, in which case there will be water vapour - hartzburgite reaction to yield more hydrogen. Serpentinization of the rock will proceed, involving about a 17% rock expansion. The rate of such a reaction will be limited by the amount of water vapour in the hole. A by-product of the reaction will be moisture at pH12 which will rapidly react with the high partial pressure of CO2 to produce carbonate encrustation. So it will be a problem to keep the hole clean - unless you prevent any moisture entering the hole from the surface control area.