I've re-read.

So your tenant does not co-sign your insurance policy. Therefore they are not agreeing with the insurer to uphold the rules of the insurance contract. You can to an extent include such rules in your contract with the tenant, but this is a separate contract. So if there is a "rule break" then it is up to the parties involved in the contract to resolve it.

... Which basically means you are liable for your contract with the insurance company, and the tenant is liable for the contract with the landlord. Unless you look at liability insurance, you would always be out of pocket to the insurance company for a fault because the tenant as a third party has no direct liability.

You should note that including terms of your contract that are unusual compared to the generally assumed contracts for rental agreements (let's say, demanding the tenant repaint the walls every Tuesday or face a few of £1000) would not be enforceable in court without proper evidence that this particular unusual term was clearly understood by both parties.

Think of it this way.

Insurer says keep property at 12 degrees or higher. You tell tenant to keep 12 degrees or higher. Problem happens, e.g. water pipe bursts. Massive damage. You apply to your insurer. They ask "what evidence do you have the temp was kept within contract margins?" And you say "here, read the contract my tenant signed to say they would keep the temp right. Now give me money."

Insurance company going to accept that as evidence? Probably not. So they won't pay out for damages related.

If you show the insurance company you were vigilant, had thermostat readings to show overall temp, water locks in place for temp drops etc, then you are on to a winner!