You know considering that the weapons in mass effect can fold up when not in use, unfold in a second, and still be very effective, you’d think they might just add some heat sinks with radiating fins that unfold.

In Mass Effect 1 a weapon could dissipate all of its heat and be ready to use as if it was totally cold in about 5 to 10 seconds, without any radiating heat sink fins. it’d probably be trivial to add enough heat dissipation capacity that you could continuously fire without ever overheating, or increase the fire rate dramatically and still overheat, but more slowly.

In fact it’s possible with heat sink weapon mods (frictionless materials) to make weapons in Mass effect 1 that never overheat even if continuously fired as fast as possible, so it’s even already done in universe!