Tenant demanding I fix one radiator that is not working

[Kevin Nolan]

BACKSTORY: I'm a new landlord who inherited a very high maintenance tenant who was on a month to month term. I made the big mistake in fixing the requests she "demanded" because I thought it was the right thing to do. Then I started receiving texts from her every other day requesting something new.

After I agreed to sign her to an annual lease the very next minute she texts me to tell me that the radiator suddenly just so happened to "stop working". I thought it was very suspicious that she waited until I signed a lease with her to then suddenly have the one radiator be broken. I'm 99% sure it wasn't working before but didn't want to say anything until she was under contract. Anyways, I called the HVAC professional to come in to try to fix the issue. He told me that the living room radiator in the unit is the only one that isnt working, but the rest of the house is warm and heating properly. I asked if it was an urgent matter to get a plumber in to fix the one radiator and he responded "Not a urgent matter at all that house is hot I had to take my jacket off that zone just had no heat to it".

The very next day the tenant texts me "Please let me know when someone is going to fix the living room radiator? Apartment is cold". 

Would someone be able to explain my rights with this? Do I really have to go in and fix this radiator if the rest of the house is heating perfectly fine? I'm worried I'm getting walked over on right now and it will only get worse. I am also sending her a text tomorrow notifying her I'm no longer accepting texts as a way of communication unless its an emergency, setting office hours, and that all repair requests will be needed to fill out a work order request and email to me.