Call them, they will answer your questions. To my knowledge, every day that you are without the heat, when you take him to court he has to pay you for inconvenience. Open Escrow account and put rent money in there every month, send him notarized letter that if he does not fix within a certain time you will withhold rent and take him to court.
You have to report them to L&I. The soon you do, the sooner you'll have heat.
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