I had the same issue with running tube amps in the summer as yourself. It was resolved with a Class A , Audio Note Soro Integrated amp.
Actually Both the Audio Note Oto ,or Soro tube integrated amps would be possible options for you to consider.
I live on the top floor of a condominium building where running a tube amp in the summer time was an issue. I would have to switch to a Solid State amp in the summer time.
The Audio Note Soro amp resolved this issue for me and sounds fantastic. It could be different for you considering the AC does not reach that well in your listening room.