Gurgling sound and radiator starts boiling even after shutting off

This means we have an overheating condition so we need to start with pressure checking the system to find out if we have a leak.

Here is a guide that will show how to do this:

https://www.2carpros.com/articles/radiator-pressure-test

It should hold pressure for many hours so let's check it and see what happens.

However, if it holds pressure then we need to make sure the cooling fan is operating because the revving up may be a fan blade being cracked or otherwise have an issue.

So we need to check this and then we need to check the compression and head gasket. If you have compression getting into the cooling system then this is going to cause the same issue.

https://www.2carpros.com/articles/how-to-test-engine-compression

https://www.2carpros.com/articles/head-gasket-blown-test

Please run through this info and let us know what you find and we can go from there. Thanks

Well, the vehicle isn't using or leaking any antifreeze so this wouldn't be a head gasket issue, would it?

If you are not then probably not a head gasket but that would be hard to know for sure if it is pushing coolant out of the radiator because you have to add more back in.

at this point, it is always a good idea to check the basic system operation. The gurgling noise is a sign that you either have air in the system or getting pressure introduced from the engine compression.

Look at step one on this guide:

https://www.2carpros.com/articles/vehicle-bubbling-noise

Hopefully you are correct with the lack of any coolant loss that it is a thermostat issue but just because we hope it isn't something doesn't mean we should not check it and confirm the head gasket is not leaking. It is an easy test with a chemical tester.

Please let us know what you find with this. Thanks