As a temp. fix you could simply lock the car but pushin down the lock pin/plunger on the door. This locks the car but does not arm the alarm.. locking with the remote or pressing the power lock button on the drivers door (while open) will always set the system..
Also the facotry (ford) alarm sytem is a basic alarm and does not measure heat or anything like that.. when the system is set It "guards" all doors, trunk and hood. If any of them are opened without a "valid" unlock event the system will trigger (flashing hazards-horn honking)
So the problem involves one of your door, hood or trunk sensors thinking that a door hood or truck is being opened when its really closed.. what you have to do is narrow down which sensor it is that bad and get it replaced. Most of time its the hood sensor thats tripping the alarm. the dealership can actually look up the last alarm event and they can scan which sensor set off the alarm last.
hope this helps ;-)