Honestly, much of the game is a bit contrived, despite all the pointers about the game being "an immersive and realistic experience"; heat sinks are no different.
A small heat sink in a utility slot is not going to drop your ships heat....at all. It's just too small. Think of the radiator in your car/truck/computer; it's not small ( compared to what its drawing the heat away from ). And miniaturizing the tech isn't really a question, because we're talking energy molecules here and the needed surface area / storage space to contain/transfer said energy.
The question about the internal "passive" cooling system should be the real focus. How is the ship maintaining ship cooling at all? The reactor holds in all that energy/heat just fine yes? Then why is the rest of the ship not built with the same materials / methods. A beam weapon should do little to nothing to increase heat to the ship, especially since it is projecting heat outwards away from the ship; and the hardpoints are always deployed outside the ship. The only thing left "inside" the ship is the power cabling, which should be no worse ( if not better ) at shielding the ship than the reactor does. And since we are talking "electricity" at this point..there should be no radiated heat coming from the cables at all. How is it my computer cables are cold to the touch..but the graphics card is hot magma? Exactly. If anything, the game needs separate heat damage for hardpoints, instead of tying it to overall ship heat. A heat sink is doing absolutely zero in that regard.
It's interesting that the ship utilizes zero ionizing techniques instead for cooling; it's like they never had one of those "junky" infomercial fan-less heater/airconditioner units. ( The name escapes me ). And in that regard, what is happening to your oxygen supply with all that heat dispersion? If the ship has a lucrative filtering / replenishment system for your oxygen, it can afford a basic fan / cooling solution to "air cool" your ship. Or even use liquid cooling to more efficiently disperse heat to the outside of your ship, instead of it just bottling up like a sauna.
Then there's the obvious practical application of shielded material. Nothing outside of the sources and transfer material of energy should be conductible. Wall panels and frames should be preventing heat from leaking into other compartments; and electrical should already be protected via capacitors and whatever minimal cooling system it has in place. There shouldn't be any "extra" heat build up just because you fired a pulse laser or got close to a star. The hull and internal plating (or liners ) should be protecting against that long before you start taking internal damage.
And at that point...a heatsink isn't going to save you, nor are you going to "cool off" in the next 10 sec by just moving away or holding fire.
For all intent and purpose, you're either flying the universes biggest solar umbrella, or baked potato.