I'd guess the opposite, actually. Mass is extremely important for a rocket, so there would be strong incentives to make the cooling system as light as possible.
But a passive system has a few major advantages - it's maintenance free, unlike an active system (imagine having to fill up the coolant tank before launch), and perfectly reliable. Sure, a phase-change coolant might be more efficient - but with flight times in the hours I'm not sure that the difference would be enough to compensate for the complexity.
Once the liquid electrolyte was injected into the batteries and the missile powered up at launch time, it was only going to be operating for 30 to 40 minutes. So it didn't need a lot of cooling capacity.
Remember this system (including power supply) replaced a really ancient system that weighed twice as much. If anything, the heavier PS was helpful because it + the support truss brought things back to the mass that the missile was originally designed around. Otherwise it would be necessary to extensively retest an old missile with limited inventory, possibly even changing the guidance equations.
But a passive system has a few major advantages - it's maintenance free, unlike an active system (imagine having to fill up the coolant tank before launch), and perfectly reliable. Sure, a phase-change coolant might be more efficient - but with flight times in the hours I'm not sure that the difference would be enough to compensate for the complexity.