Why space heaters don’t satisfy the duty
No. A landlord generally cannot satisfy the duty to provide heat by telling you to use your own space heaters. The landlord must provide working heating facilities, not push that responsibility onto the tenant.
Portable space heaters are a temporary stopgap, not a substitute for the permanent heating the landlord is required to maintain. They can also raise fire and safety concerns and add noticeably to your electric bill. If your landlord's answer to a broken furnace is "just buy a space heater," that usually does not meet their obligation to keep the home livable.
Document the response and keep reporting the problem in writing, since a landlord relying on your space heaters is still leaving the heating duty unmet. If your landlord expects you to supply your own heat, a free, confidential review can help you understand your rights.
This is general information about California tenant rights, not legal advice. Every situation is different.