This makes little sense to do on the scale of a single computer that may draw 100 W.
However, this has been done on the scale of whole buildings. Buildings that are designed expecting high power dissipation in some rooms but not others often have air conditioners or heat pumps for cooling/heating individual rooms or small zones. These tie to building-wide water circulation systems.
The heat pumps that heat/cool individual rooms or zones take/dump the pumped heat from/to water circulating to a central pool. A building-wide system keeps this pool in a controlled temperature range. When the building needs overall heat, then the heat added to the pool from those zones that are being cooled reduces the deliberate heat that is added to the pool by the central system. So yes, in that case the heat from computers, and anything else that dissipates power, is re-used to warm other parts of the building.