My lease specifically forbids auxiliary heat sources like space heaters, plug in radiators, etc....and with good reason.
While maintaining client confidentiality - I say this a few days after inspecting a 100 unit building that had to be completely evacuated, over a dozen people hospitalized, and now has about $1 million dollars in damage all "allegedly" caused by....1 tenant who "allegedly" put a space heater on a bed and left it. Let me repeat that - she "allegedly" put a space that heats with a red hot, fire starting element right onto a cloth bed.
Because of this one tenant, the insurance premium on this structure is going to see a significant increase - in other words, bye bye cash flow. Don't go soft on tenants over seemingly little rules like this. There is a very good reason for it.