I have a Cool Fire 4(40W no TC) that I use regularly at 35-40W with 2 or 3 different RDAs(rebuildable dripping atomizers), I have never used the Isub tank. That said, I dont think you're having a compatibility issue here. If the coils you're using are made for the Isub tank then they are compatible with the tank. If your mod will recognize the tank and it is producing some sort of vapor then the tank is compatible with your mod. Most
tanks, RDAs, RTAs, Gennys, etc are compatible with most mods unless firing at resistances too low for the mod chip or battery(see mech mods) to handle.
There are many contributing factors to an atomizer heating up, and for the most part it is normal to experience some heat after a vape. How much heat is dependent on how frequently you vape, how much power(wattage) you're pumping into your atty, the resistance of your coil, the airflow settings that you're using, etc.
If you are having connection issues(especially regarding compatibility) then I dont think the Cool Fire 4 would fire. For me it just throws out an error message saying "check atomizer" when there is a connection problem. For this reason Im assuming that the heat you're experiencing from the base of your atty is just excess heat from one of the many factors which are all relatively normal.
If you are really concerned that its too much heat then lower the wattage some more and see if that helps, open the airflow some more and see if that helps, wait longer between draws and see if that helps, try using a spacer like the one I linked to earlier(many vape shops carry them and have them on hand for around $5). If all that fails, then go back to the coils you used before this.