I’m quite tired due to my own NHS based life at the moment but i think it is hard to see how your wife does not have a really very strong case here. Either the radiator was faulty or the supervision was faulty the Nhs are ultimately liable for both. So your ambulance chaser sues the NHS and they join in the contractor the judge awards damages to your wife and the NHS and contractor fight each other over how much each pay.

She has three years from incident to make a claim