> generating heat with electricity is expensive

God damn it, it is not ok to be this uninformed this far into the climate crisis. Heat-pumps are about 400% efficient now and work down to -20 for the latest models.

Remember, heat-pumps generate NO heat whatsoever, they simply move heat from one location (often the atmosphere) to another (like your home or hot water tank). It is energetically much cheaper to move heat than to create it. Thinking of it like that, the sun is what is doing about 80% of the work when you use a heat-pump.

Burning gas or anything else on site will be 4-6 times less efficient, even if you are getting all your electricity from coal (you most likely are not).