Legal Question in Real Estate Law in California

Contact your city or county government and find out where to file complaints about unhabitable dwellings. Then file a complaint. If the government finds a habitability problem (lack of heat qualifies) then they will issue a citation to the landlord. If the landlord then does not fix the problem, you will be entitled to break your lease and the landlord will have to pay you relocation expenses.

Look up and read Civil Code sections 1941.1 and 1942. The first covers conditions that make a dwelling unit "untenantable," and the latter covers a tenant's right to "repair and deduct."

Basically, within certain limits, a tenant may make necessary repairs and deduct the cost from the next rent due.

I would think that if the lack of repairs is preventing you from getting hot water safely at your shower and sinks, or the water heater is not earthquake-protected as required by law, you'd be entitled to do a repair-and-deduct. However, any defects with a lesser impact would probably NOT qualify.

Sorry, I mis-read your question. You said "heater," I incorrectly assumed "water heater." However, the same principles would apply to space heating as to water heating. If the space heating equipment doesn't safely keep the place warm, follow the CC 1941.1 and 1942 procedures to repair and deduct the cost. Be sure to notify the landlady, to get a receipt for the work you pay for, and to otherwise document the problem and the cure in case there is a dispute about whether your place was really "untenantable" or not. Having friends witness the lack of heat beforehand would be a good idea, for example.