Sam M New Zealand

I'm about to buy a 2001 E38 728i, I have owned a E65 730i and F02 750Li here in New Zealand. Any advice for the E38? The radiator has been changed, thermostat, full serves current owner has had it 6 years. As he's rebuilding a E30 he has no time to look after the 728. She overheats underload. When I looked at it. Had it idling 20 min and nothing was hot to touch. No white smoke etc. no water in oil etc. what would you say it might be. ? thanks sam m New Zealand