As posted by another user, the warm case means exactly the opposite. It is getting warm because the heat source is well connected to the case thermally. I suspect the PSU is the culprit, but cannot be sure. CPU temps seem well controlled but certainly not ambient. I think it all boils down to a small unit with a lot of electronics and it gets warm. Whether this causes premature failure is yet to be determined. It would be nice if Apple published typical case temperatures indicating design criteria.Sounds like maybe you have a mini with a poor thermal paste job done on it.
Don't know your skill level, nor the complexity of taking apart the mini, but repasting may be an option