You're hassling the wrong people. Your statutory rights rest with the retailer, not with the manufacturer, so it's that retailer that you should have contacted.
After a couple of years, you're in the position where the retailer is responsible for rectifying any fault with the appliance that was present at the time that you bought it. (e.g. the inclusion of a poor quality component or the use of a poor standard of workmanship).
However you've now gone past the point in time where there would have been an automatic assumption that any problem that occurred must have been be due to such an 'inherent fault'. If you want to claim from the retailer now you'll have to show that, based upon the balance of probabilities, the most likely reason for the problem occurring is that there was poor workmanship or a dodgy component. It's sometimes possible to do that simply by challenging the retailer to suggest any other reason why the appliance might have failed but, if you want to try to go down that route, you'll need to be prepared to do a lot of hassling.
Otherwise, both the retailer and the manufacturer are both perfectly entitled to tell you to get lost. The threat of some bad publicity on review websites, and on social media, can sometimes work wonders though!
My own feeling here is that is, indeed, almost certainly a thermostat problem. It might be worth looking on Youtube for instructions on how to fix it yourself and then checking on the price of a new thermostat. If a replacement thermostat would cost you nearly ninety quid anyway, it would seem to make most sense to accept the offer of having an engineer come to replace the dud one. However if you can buy a thermostat for far less than that, go down the DIY route.