Could very well be the flasher going. The mechanical flasher relies on heat to make it operate - normally, this heat comes from the current flowing through it. If there isn't enough current, or the flasher is going bad, it won't heat up enough to actuate it. With the added heat from the engine, it might be enough to "tip it over" and make it work.
It could be caused by a faulty connection to some of the turn signal lights. Does it happen both turning left and right signals on? If it only happens on the left, then it's likely that one of the +12V wires going to one of the left lights has a bad or corroded connection somewhere. If it happens for both the left and the right, it could be the ground connection for either the front or the rear (the front shares a ground, and the rear shares a ground). In that case, check to see if the front or rear turn signals seem dim. You can check this by removing a bulb and putting a multimeter across the contacts in the socket - if you're seeing less than 12V then the ground on those sets of lights could be bad.
Or, it could be just a bad flasher. Try replacing the flasher with a mechanical (not an electronic) one - if it still happens, then you've definitely got a bad connection/ground somewhere. If it fixes it, then that's what the cause was.