you need to check your tenancy agreement,i would think your landlord would be responsible for replacing the radiator but you would probably need to claim on your contents insurance for the carpet
What I assume is typical lettings policies is the landlord has buildings insurance, and a small amount of contents (which covers curtains, beds, tables etc)
The tennant is expected to have insurance for their stuff
Thats how the lettings policy the company I work for do it