Not for nothing but could one see power dissipation across a fuse with a thermal scanner if the current is just - say - 40 mA?
I'm assuming some normal batter so somewhere around 40 AH and let's assume that drains over four days to being dead as a door nail. That's 40/4 = 10AH per one day. That's 10/24 = 42 mA.
LEt's assume the fuse is a horrible fuse and has an internal resistance of 0.1 Ohm.
That means that the actual power dissipation of that fuse is 0.42 * 0.42 *0.1 = 0.2 mW and I'm being generous with the numbers, rounding them before calculating.
You can't see 0.2mW on a wire.
There won't be any appreciable amount of heat dissipated by the wire. The fuse is in an outside area (in cold Alaska no less!) and it wants to be at ambient temperature.
You'd have to drain a lot more current than just 40mA. If the dealer can't find where some parasitic drain is going, they have no business repairing cars, let alone putting remote starters on.
There's no way that car shouldn't last for weeks if left alone. Sure, Alaska is cold but your summer is probably still warmer than our CT winters. We leave our cars in long term parking all the time at the airport for weeks on end without any issues.
I agree with the other suggestion of disconnecting the remote start fuse first. Actually bring it to the dealer and make some noise. They clearly are morons.