Rocky - you may find
this link better for the 'layman'?
Trying to remember back to the dim and distant days of met THEORY, above the tropopause the temperature is assumed 'constant' with altitude, whereas below it cools with it. I recall that where the tropopause is LOW, ie in the Arctic, the trop temperature is therefore relatively higher and therefore the 'constant' temp above will be relatively higher. 35000' will almost certainly be ABOVE the trop in the ARCTIC. Where the trop is high, ie the tropics, 35000' will probably still be in the troposphere, so still in the 'cooling' part, thus it will be colder at 35000'.
Para 3 of the link "This explains the paradox that tropopause temperatures are lowest where the surface temperatures are highest. " suggests I might not be too far adrift?
Over to the Met teacher for marks out of ten!
Edit:: never mind the met marks out of ten - I couldn't spell ARCTIC!