Alright, keep the coolant mechanic, but make people purchase it, like you have to in CBT. Coolant pods are bulky, limited use items that have a tendency to explode violently when shot. This would be akin to purchasing jump jets for a mech, or additional ammo for ballistic weapons. The player has to make the choice of whether to spend precious tonnage on some coolant pods, or to rely on proper fire discipline and good piloting to avoid unnecessary heat spikes that may cause shutdown or a horrible melty death.
The other option is to remove coolant and then rebalance the weapons so that they take into account that you don't have coolant to instantly flush away your first 5-10 accidental heat spikes.