Ok, the question is if you could build an oven heated by a heat pump? Yes, you could.
You can reach home cooking temperatures reasonably easily, and probably even large ones. It's helpful that the compressor only has to deal with gases after they got cooled and heated again on the open air, all the really hot parts are rigid tubing.
There will be problems turning the compressor off, dealing with the heat that propagates back through the pipes. You can solve them with some usual cooling devices (heat disipators, fans, etc).
