So. If you want to take shields with at least two A-garded boosters you'll need some powerplant engineering to carry 2 medium gauss. If you have armored 1 with monsterd you should have no problems taking every shield except prismatics. If you really want to fly prismatics then you need a bit more engineering on your powerplant. Armoured grade 4, monstered, or overcharged 1, monstered will be necessary.
Gauss cannons built up a lot of heat. I think ther is no ship that won't get some heat if you fire them in short succession. If you fire them with some care, you shouldn't have any problems though.
The asp is the second coldest running ship in the game so yes you could if you engineered it right. The thing is you cant use more than 4 experimental weapons at one time and you can't engineer the gauss canons either. They are also much hotter than regular rail guns. Normal weapons are effective against scouts also so keep that in mind. You might also consider using normal rails (if you arent going to go after the interceptors) and have experimentals on them to lower heat. I dont recommend you fight interceptors in an asp.