Thank you everyone for your responses and advice! Here is an update:
I have spoken back and forth with the tenant all day, I told him everything that was going on on my end. I had called the warranty company, asked for other options (fronting the cost = reimbursement?) I reiterated that I need someone out there asap, and they weren't very understanding. So I called the tenant and he was understanding but disappointed. I told him that the temperatures are looking pretty great over the next few days and he should be okay. I told him I would buy him a space heater if he wanted one. He said that he will see how everything goes tonight and let me know in the morning.
I think it helps living in the other half of the duplex because we have built a good relationship. He knows I am not taking it easy and am putting it as a priority. I feel if I was a distant landlord and didn't know the guy that well, he might have put up some resistance. I will make a post on the entire situation on how the home warranty situation works out once everything is solved. I feel like this makes for a good topic on is a home warranty worth it? Once again, thanks everyone for your responses, it is very much appreciated.
@Alexander Felice @Christopher Finn @Kyle J. @John Underwood @Cara Lonsdale @Nicole A. @Corby Goade @Matthew Paul @Christine Kankowski @Nathan Gesner @Thomas S. @Robert Cheek @Account Closed