Abstract: Only a gap defining the outer profile of the tunnel or borehole is melted down in a peripheral heat drilling process for tunnels, deep-well and exploration boreholes. The drill core, surrounded by the generated gap, initially remains and is then extracted at intervals via a tube. It is expedient for the drill core to be sheared off and extracted continuously after it has passed a cooling zone. The height of the drill core, which first remains in the borehole, is determined such that the molten rock can be pressed into the drill core, whereby the necessary pressure for this pressing in is maintained essentially constant, independently of the depth of the borehole concerned.