Described is an assembly for an internal combustion rotary engine of a single or multi-rotor type. The assembly includes parts without cooling channels that comprise a monolithic ceramic material or ceramic matrix composite material capable of allowing the engine when assembled to operate at elevated temperatures that would cause metal parts of a metal engine to lose strength, lose structural and mechanical integrity, suffer excessive oxidation/corrosion and/or fail. The ceramic material also allows the engine when assembled to operate with significantly lower heat loss to the surrounding environment as compared with a similar engine made using all metal parts. The ceramic material allows the engine when assembled to operate without requiring substantial cooling elements or an external fluid (e.g. water) cooling system. The engine when assembled as described will retain more heat or operate with a substantially reduced rate of heat rejection when compared to an entirely metal rotary engine.