For example what happens if you use your mechanic's energy shield and have a force field armor upgrade?
You add the new source of temporary hitpoints on top of the existing, but you have to keep track of ones that have a time limit.
Energy shield lasts 1 minute per Mechanic level at its base so you would simply add the temporary hitpoints from the force field armor upgrade until the time from energy shield ran out (or enough damage is taken to remove the temporary hitpoints) and then you subtract the amount from energy shield from any current remaining temporary hitpoints.
So for example:
Let's say as a Mechanic 2 with a 16 Int you activate energy shield. You get 3+2=5 temporary hitpoints. It lasts 2 minutes. Let's say 1 minute later you activate a purple force field for 5 temporary hitpoints. Then you now have a total of 10 temporary hitpoints. 1 minute later, energy shield ends and you now have 5 temporary hitpoints from your force field.
As far as determining which one gets hitpoints taken away when you are attacked and both are active? Typically the newest one gets it taken away from when attacked. So let's the same scenario above and you get hit by a laser pistol for 3 damage. You would take 3 temporary hitpoints from the force field and your energy shield would still have 5 leaving you with a total of 7 until 1 minute later and your energy shield ends and you now have 2 left from your force field.