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I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
The terms of the lease control, even if the landlord dies. The lease transfers to the new owner of the property. "Heat" means heat provided by the heater in the unit unless the lease says otherwise. The landlord cannot raise the rent in the middle of a leased term, unless you're month-to-month, she cannot raise the rent $66/month (and even then, she has to give notice). The type of heat is going to be controlled by the heating unit on the premises. The landlord can't require the tenant to use space heaters or electric heaters rather than the house's full-sized heating unit. The tenant would have no ability to object if the landlord were to replace the furnace, nor can the tenant require the landlord to change the type of furnace already in place. If there's something like wood-burning stove, the tenant is allowed to use that, too, unless the lease says otherwise. If you're talking about something like space heaters, check the lease - they are often prohibited because it can be a fire hazard when a tenant falls asleep while using them.
But "the landlord will provide heat" usually means "The landlord will pay for the heat bill for heat provided by the furnace."
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