My landlord charged me with the repair of the furnace claiming that a thermastat I replaced burned out the wiring. I'm OK with that but, he is waiting until after the new year to give me the bill because he is going to pay the heating and cooling company that did the work, then use the repair as a tax write-off. I wanted to know is that legal for him to do that, then turn around and get compensated for it from me?

No. If you are paying for the repair, then he can't claim a deduction for it. However, neither can you because you don't own the property.

It depends upon the method of accounting he uses. If he is on a cash basis, sure he can deduct the expense in '12, but will have to declare it as income in '13.