The fact that the sensor is on for about 95% of the time through that process means that the heat isn't any different than a mirrorless setup.
Dark frame subtraction corrects reasonably well for this anyway. Cooled camera would perform better but that's a lot more trouble than it's worth for me as a hobbyist. I wouldn't recommend cooling with ice packs though. You want your sensor at a constant temperature through most of the data collection so that your dark frames actually work. If the temperature of the sensor fluctuates, your dark frames become not representative of the actual dark currents most of the time.