I would check the most obvious. faulty closed stat will cause it to creep. but I would check my clutch fan first. these are not uncommon to go.
Rule of thumb. go with the cheapest. remove the stat - test it in boiling water to see if it opens. if good. re-install bleed the system thoroughly or you will get the same result.
if the problem persists -next clutch fan.
I'd find out from previous owner to see what's been replaced recently.