Hi, I had this and the odds are the radiator is blocked at the bottom. They do this regularly and the only way forward is to either take the rad out and thoroughly flush it through or if funds allow to replace the rad altogether.
With regards to the fault code, this wouldn't throw up the engine fail safe message / light. I have replaced my thermostat with the 80 degree mod and as such you have to disconnect the multi plug for the thermostat heater so I have that fault all of the time but no fault message or light.
What other messages do you have? With mine I was getting trans fail safe, HDC inactive and the suspension was inactive after about 5 minutes of driving, it turned out that it was the abs module going bad. Swapped it out and everything was fine.
Range Rover Classic 3.5 efi - Gone
Range Rover Classic 3.9 efi - Gone
Range Rover Classic 4.2 LSE - Sadly gone
Land Rover 110 3.5 - Gone
Range Rover P38a 4.0 SE - Pleased it's gone
Range Rover P38a 2.5 DHSE - Just sold
Range Rover L322 4.4 v8 Petrol - Current