It does sound like the thermostat has failed if the radiator is not getting hot at the top.
It is located at the engine end of the top hose. In the housing there.
Be aware that the 4 x 7/16" bolts can seize and pull out the thread when you try to remove them ~ so do the job somewhere that it may be stuck for the day without inconvenience. We always have a 3/8" unf helicoil kit at the ready. If it all goes smoothly it should only take about an hour.
We prefer and supply the 'lead shot' type thermostats. The lead shots melt and allow water to flow through the radiator if the thermostat fails closed or the coolant gets far too hot. About £55 inc vat & UK postage.