Help: problem with noise in my axis super sport

My house has electric wall heaters which are really common here in France. When I plug my super sport into my katana 50 or my laney lionheart, I get this loud electric noise coming through. When I turn the heaters off, the noise goes away. When I plug my standard american strat or les paul copy with classic 57 pickups, there is no noise at all. At least not the electric noise from the heaters.

I’m assuming that it’s the high gain pickups of the super sport. I am very emotionally attached to my super sport. I play it 3 or 4 hours a day unplugged when I practice.

What can I do? And no, it’s too cold to turn off the heaters.

thanks
Nick