Having all-day heating, I meant it to be available, not necessarily that it be on continuously. A few hours in the day could be enough. On a day where temp is around 0 though you might well want it continuously. I'd never have it 24/7 though, I'd want it off at night.
The rent is overpriced already. I wouldn't ask to pay more.
I realise now it should be controlled by the tenant, but that isn't set up here. It's controlled centrally. It would probably mean changing wiring etc to set up which I don't think he'd agree to.