You don’t need a cooler, just a vial of liquid nitrogen or dry ice. If the gun was air powered rather than fired with gunpowder the heat issue would be substantially reduced. Also the dirt didn’t need to be fully solid at time of impact to effectively poison the target, as all that was needed was liquid contact with the skin.

Also everyone here seems to be pretending that flachette rounds aren’t a thing and weren’t proposed to replace bullets as the primary rounds for the standard issue rifle for the us military as recently as the Advanced Combat Rifle program to replace the M16. AAI’s flachette rifle went all the way to final testing and consideration, and was easily accurate at 100m and beyond. This weapon shot single darts aka flachettes and would have no problem with achieving accuracy at 30m with a shorter barrel.