As was already applied, there really is a giant surplus of heat sinks in that level - in pretty much every level, to be honest. Since you're using an assault rifle at that early mission, I'm assuming you're playing a Soldier. You might prefer to use the AR, but as a Soldier, you're giving up powers for the ability to make use of every weapon but a sub-machine gun. And the Archangel mission is a good example of strategic use of the different weapons - in the basement, for example, you should probably want to use the shotgun and/or pistol because everything's coming at you and it's relatively close-quarters.
There is/was a weapons locker right before you head down to the first basement door, so you could have swapped out the Vindicator (AR you picked up) for your old AR, had you wanted to. Alternatively, you should learn to use the Vindicator well, which is to say, learn to squeeze off head-shots. Adrenaline Rush + Vindicator headshot = dead everything.
If you're running out of ammo that quickly, you probably just need some practice shooting straight. You'll get better at it.
Regarding heavy weapons, ha, I barely even use them on my Soldier. I remember making judicious use of the Cain during my Insanity playthrough, but that was really just to nuke the two Praetorians in the game.
Yes, I'm playing my Soldier (import from ME1). The reason why I couldn't swap out the AR is because I found the new weapon near the end, after I returned to the top of the apartment to see Garrus. The locker was at the basement, and the waves were about to start, so I didn't go down there. It just seems mighty inconvenient since we can switch weapons freely in ME1, but not in the sequel.
In fact, there are many changes that occurred in ME2 and made it vastly different than its predecessor. Here are some things on top of my head:
New skill system
Required to use weapon locker to change weapons
New upgrade system
New body part targeting system
No overheat/need to reload ammo
Cannot view stat on weapons
Ability to customize the color scheme of armor
No mini-map without holding of button
No access to map in the menu
No Marko
Less abilities to use per character
New ammo system
New abilities tied to loyalty
etc etc.
There are some changes that I love (body part target system, can customize armor appearance, new ammo system), some that I'm ambiguous about (new upgrade system, new skill system), and some that I really hate (can't swap weapons, less abilities, no map). Look, I've brought almost all the DLC except Overload and Equalizer Pack, and the alt. appearance packs, and overall it's been alot of fun, but part of me wonder why they made so many drastic changes. I do believe the old saying of "If it ain't broke, don't fix it". I'm not saying that Bioware should've kept everything's the same, but it seems like they weren't happy with ME1 and wanted to change the game fundamentally.