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Renters Liability in Case of Liability Claims for Property Damage or Fire
The truth is anyone can sue anyone for anything.  So yes you could be sued, but the more important part to measure is the probability of success.   While this is probably more of a legal stack exchange question, in order for a successful suit there has to be proven at least some negligence on your part in the situation you cite.  The very fact that the landlord is not willing to turn on the heat is probably enough to absolve you from any liability.  Once you go down to a local store and purchase a UL certified heater then a suit would have a very low probability of success.   Perhaps a case could be made if you made your own heater and it burned down the house.  But that would require finding a jury that is sympathetic to landlords that will not provide heat for their tenants (highly unlikely). Could the landlord sue the heater company?  Yes and would likely receive an out of court settlement.   Even in the case that liability can be proven on your part, it is very unlikely you would be targeted.  These type of suits target "deep pockets" or those with wealth.  Unless something is specifically known about you having a high level of net worth a civil suit will not be brought against a "room renter" because of the lack of funds.  People in your demographic tend not to have a lot of money.  (No offense intended, I was there myself once.)  In the case that you do have a high net worth, then get renters insurance and possibly an umbrella policy.  It is a small price to pay to protect a significant amount of assets.   If I was in your shoes here is what I would do: