He's a Time Lord (body temperature around 16 C/60 F) who's masquerading as a human, and needs a convenient excuse for why he's so cool to the touch. It doesn't need to stand up to any intense investigation, and he does avoid contact when possible.
Would 'poor circulation due to a heart condition' be sufficient? (For various reasons, he would find it very amusing to have it be somehow related to a heart problem.) Or do I need something more elaborate? It doesn't have to be a perfect match (especially not at that low a body temp), but just something he can toss off to stop people asking questions.
Place and time: Britain, modern day
ETA: Looks like it's Raynaud's Disease or Phenomena to do the trick! Thanks everyone!