Can I Dispute The Transaction?

Hello everyone.

I have recently stayed at a resort in France which I booked through Booking.com. The resort clearly listed heating as one of the amenities they provide. However, for 4 out of the 8 nights I spent there, the heating was not functional. As the temperature outside was around 10 degrees celsius at night, this heavily affected the quality of my vacation. It should be mentioned that I contacted the resort about this during my stay but it took them a very long time to provide adequate heating.

I have told them I want a refund for those 4 cold nights, and they told me I need to file a request with Booking.com. I did, and Booking.com told me the resort has refused the refund and there’s nothing more they can do.

Can and should I dispute the transaction with my credit card company? I’m assuming the resort will lie and say the heating did function. The main proof I have that it didn’t is my messages to them throughout my stay complaining about this. Do I have a case?