Car starts when cold but cuts off when warm?

Hi there, I have a Toyota Estima Aeras 2.4L Petrol Automatic transmission JAP Import. I’m based in the UK London. I bought this car a month ago and it was driving perfectly fine until the cold snowing weather where the car misfired a couple times as it struggled to start.

It then started and I let it run and everything was going okay. I noticed the heating within the car was getting weaker and gradually letting out cooler air and then there was no heating in the car through the vents at all. I then noticed the car had a new overheating issue, so I then checked under the hood and realized I had a low coolant levels which I later found to be a leak as I topped it up, but it drained within hours.

This then meant the car would start and then cut off minutes later. I got it to a mechanic and got the following work done:
Leak fixed by new adding brand new radiator
Ignition coil
Spark plugs
Throttle body (was a nightmare trying to source this part)
Crank shaft sensor (I tried both aftermarket and original Toyota for this part and both had same result)

Now the car will start when it’s cool and run until the engine gets warm (even whilst idle) and will cut off as soon as the car gets warm. It isn’t any longer an overheating issue I’ve been told but just cuts off after warming up. We then have to let it cool down for a long period and then start it up again which it will do. My mechanic doesn’t know what else to do, someone suggested a new thermostat, but I don’t know as my mechanic said that’s not the case, what?

Does anyone have any suggestions of what it can be as the cars been at my mechanics for over a month and been nothing but trouble, they can’t diagnose it either as apparently it doesn’t work.

Any help would be hugely appreciated, many thanks.