Abstract: This temperature regulation apparatus comprises a heat pump (12) comprising a main compression circuit (14) for a refrigerant fluid taking heat from a cold source (16) and transferring it to a hot source (18). The cold source (16) comprises a first heat exchanger (24) for exchanging heat between the refrigerant fluid and a liquid coolant thermally coupling the main refrigerant circuit (14) to a first secondary coolant circuit (26). The first secondary circuit (26) has selective connection means (40, 52, 54) for selectively connecting it to the upstream and downstream ends (48A, 48B) of a “heater” branch (48) of a cooling liquid circuit (46) of an exothermal part of the vehicle. The exothermal part is preferably a heat engine of the vehicle. The invention is applicable to air conditioning a motor vehicle cabin.