Digging depth and heat
The heat equilibrium depth will vary for different locations due to:


Differences in geothermal gradient at different locations (heat emitted by rock). It is generally accepted that the global geothermal gradient is between
${25 ^o C/km}$ &amp; ${30 ^o C/km}$. At some locations the gradient can vary between ${15.4 ^o C/km}$ &amp; ${102.6 ^o C/km}$.
The temperature of the air will increase with depth due to
auto-compression of the air (also known as lapse rate). [Environmental Engineering of South African Mines, 1989, pp 403-404]. The increase in dry bulb temperature of air due to auto-compression is ${9.66 ^o C/km}$, if there is no change to the humidity of the air.
Moisture content of the air. The greater the humidity, the greater
the heat in the air.
Ventilation of the hole being dug and how much heat the moving air is
removing from the bottom of the hole.
Temperature of the air entering the hole from the Earth's surface
The presence or absence of other sources of heat such as machinery, electrical equipment, warm water springs entering the hole and warm bodies.
The age of the hole and its exposure to ventilating air. New holes expose fresh warm rock to air in the atmosphere and the air eventually carries away the heat via ventilation. New holes, or new extensions to holes, are warmer/hotter than old holes.


The shape of the hole will be determined more by its function and geotechnical conditions, such as ground stability, than temperature.