A liquid or fluid cooled housing of a rotary piston internal combustion engine of trochoidal type of construction consisting of side parts and a dual-arc housing inner surfacing and having an eccentric shaft passing through the side parts. A triangular piston rotates upon an eccentric mounted on the eccentric shaft and corners of the triangular piston are in sliding engagement along the housing inner surfacing. A connection tube is provided supplying cooling medium into the individual housing sections. A series connection of the cooling medium circulation is produced between a first side part in direction of cooling medium flow and a first housing part as well as between a center part and a second housing part respectively having a closure disc installed therewith. Perforations are provided for pressure equalization in the closure discs. For production of a parallel connection of cooling medium circulation between a first side disc in a direction of cooling medium flow and a first housing part there is installed a shutter and further shutters are provided between the first housing part and a center part as well as between the center part and a second housing part in flow direction and between a second housing part and a second side part. Parts are interchangeable irrespective of series and parallel cooling medium circulation. A by-pass for cooling of an eccentric shaft and eccentric bearings thereof branches off independently of series or parallel connection of the cooling medium circulation.