Then you are introducing an extra thermal reservoir and it doesn’t simply provide a power P but has some temperature dependent heat transfer. You are talking about something substantially different than what I was talking about. Even in your scenario I would not say that the >0 K cold reservoir increased the temperature of the system. I would just say that it kept it from cooling as much as a 0 K cold reservoir would. I wouldn’t say that failure to decrease the temperature as much as a 0 K reservoir is the same increasing temperature. After all, I say that my clothing keeps me warm, not that my clothing warms me. As long as we are considering alternative configurations, if you have the hot-reservoir/system/cold-reservoir configuration and you remove the cold reservoir then the system temperature goes up and if you remove the hot reservoir then the system temperature goes down. So I think that the “consider alternative configurations” approach is inconclusive. I do apologize for failing to specify the scenario I had in mind completely. I would not use your description, even given your scenario. But that is admittedly semantics.