If the oil and coolant look ok, check under the oil cap. If there's milky sludge under there then it's possible the inlet manifold gaskets could be up for replacing. Does it require a top up once a week or so? My old Acclaim would beep HOT and the temp would shoot up, then come back down when I put the heater on. I checked the radiator after it had cooled and nothing in the neck. Top up and bleed, it would be good for about a week then start beeping etc again. Sludge under oil cap, so I bit the bullet and pulled the inlet manifold off. Sure enough the driver side gasket had failed around the front water jacket. About a day to replace, no issues over the next few weeks before I sold it. These gaskets are pretty common to fail on the ecotecs from about 150,000k onwards. I changed mine at 240, it looked like it had been bad for a while.
A pressure test should help determine if the gaskets could be bad, to save pulling the manifold off to find they're fine. But if the fans are working properly, and the oil and coolant look ok, then the gaskets could be worth investigating.
A split hose is another possibility. My parents had a VT that would beep and flash hot, but only over 80km/h. Ended up being a split heater hose, all good once it was replaced.
Also with the fans, if you get it up to temp so one fan kicks in, turning the aircon on will get the other one going from memory. I did this when investigating my issue above.