We need somebody to calculate heat movement through rocks.
When a part of a rock is heated about 400 degree Celcius, how fast will that rock cool down by convection.
In a deep well, how much heat can be transported away by cooling medium (for instance water) from the well before the temperature gets under 350 degree Celcius. This will for sure depend on the type of the rock (and its heat capacity), the size of the well, the heat capacity of the cooling medium, and the speed if the colling medium.
We need some general equations for this, and specific calculations to simulate different technical situations (well depth, well diameter, rock type etc)