depends what is meant by rainbow, the actual bow is light formed from the sun shined through raindrops and as such is a light show, massless and therefore temperature less as squarbear says. Perhaps the questioner means the arc of raindrops being utilised in this way, in that case I'd say definately the red bits, err know sorry the bit's nearest the big yellow alligator, err sorry croc of gold err even the ground as teddio suggests.
wtf? isnt a rainbow just refracted light? therefore having no temperature. and since light has no temperature there is no hottest part or coldest for that matter. i could be wrong though lol.