[@Shikaru]
Both would, blood is required to flow through a body for it to work, and blood can't flow cold.
Past that, even if Vampires didn't generate heat, they'd have a cold signature, unless they were surrounded by ice that matches the amount of heat (or lack thereof) that the vampire produces exactly. Either way, you would show up on a heat signature, you just might be white and blue instead of red and yellow.