This article deals with the energy analysis of a heat pump coupled to the ground to verify the thermodynamic conditions surrounding it and which makes it competitive with technologies using atmospheric air as the heat source, even in regions with mild climates. The comparison is based on the maximum theoretical efficiency available in correspondence to the temperature effectively assumed by thermal energy reservoirs in contact with the evaporator and the condenser while operating. Benefiting from the exact solution in the laplace dominion, from the response of the grout-ground system to a impulse of thermal power, it is possible to determine the point-by-point temperature trend at the probe-grout interface for whatever trend and duration of thermal loads, thanks to the discrete fourier transform. The computational code compares the electricity of two ideal carnot heat pumps operating between the environment to condition, the ground and the atmospheric air in the region of interest.