sir- judging from the symptoms, my best bet would be your auxiliary fan. what car are we talking about here, if i may ask? i ran into a similar problem before with my 6cyl bmw. ganong ganon din...idle for 10 mins or more, tumataas yong temperature. pero once the car starts moving again, babalik sa normal operating temperature yong car. i checked everything (coolant, radiator, cooling system) lahat ok...except for the auxiliary fan. the problem was that the auxiliary fan in my car was too small. replacement part na sha, and from the looks of it, parang it's size was more appropriate for japanese midsize cars. so i got a bigger fan (yong size ng fan ng mb 124), bosch, cost me 8k pero problem resolved! yon lang ang problema.

so i think it would be a good idea to check and see if you have the right size of auxiliary fan. compare with other cars of similar make and model. kung tama, check if the auxiliary fan is working properly din. possible na baka ndi sha umiikot ng tama or baka naka low lang lagi. from the symptoms you mentioned, i'm inclined to think na it's your auxiliary fan.