Tenant wants landlord to pay past utility bills when they didn’t notify landlord of issue

My tenant received very high electricity bills for the past few months. They did not notify me until January 11. I had the unit inspected and found that the heat pump was stuck on. I had the unit repaired and in good working order on January 19th.

I offered to pay for the entire utility bill from the 11th to the 19th, while it was being repaired. I also offered to pay for half of their December bill.

They have refused and are not paying rent, and want me to pay for all their past utility bills where they felt it was eccessive.

 Please advise….

 Thank you