As a gunner I'd love 'some' way of getting on overheated gun, at least to load heatsink in, if it's managable (say, those 10 stacks). Suggestions:
A) Make a tool* for gunner which would allow (partially) to ignore the effect of overheating. For example some gloves that allow you to mount guns with up to 10-15 (or whatever) stacks of fire on them.
*inb4 "gunners don't have tools, they have ammo!", hear me out at least
B) Make an automatic ability of gunner to endure overheating weapons using stamina. It would work automatically when gunner is on/mounts the overheated gun. Perhaps some UI thingie showing us that gun is overheated would be nice too.
C) Make heatsink protect the gun from the moment of reload start, not from the moment of being fully reloaded. (You can either let people abuse it or just lock the ammo change - if you load heatsink you can't change ammo up untill it reloads properly)