The answer to your question is absolutely not. (And you are right about Civil Code section 1941.1) The unit has to have a built-in heater capable of heating all the rooms to 70 degrees. The fact that there is no heater probably means the apartment is a bootleg (cut out out of a bigger apartment) and illegal. You need to call either the local department of building and safety or the county health department, and they will have the landlord cited for lack of heat and will order him to clean up the mold.
By the way, mold is not due only to the lack of heat. For there to be mold, there has to be water intrusion somewhere. Often a pipe breaks in the walls and it goes unrepaired, causing mold to grow in the walls. This is very unhealthy.
In my opinion, your landlord has breached the lease by being in violation of the implied warranty of habitability, and you can walk away. However, the landlord will probably have a different legal analysis. That's why you need to call in the authorities and have him cited.