Whew that's hot lol, but what can you expect when that momentum is converted almost entirely into thermal energy? Ever touch disk brakes after using them good? Ouch! Only reason why rim brakes and rims stay so cool is they are massive (in comparison to something like a small hub) and are capable of dissipating a lot of heat, especially figuring how much metal is seated with the spokes and nipples, it's like a giant heat sink hahaha...
Well looks like it's time for you to start converting... Never been able to rely on coaster brakes anyways... I think it has to do with when I was a child growing up in a very rural, practically deserted, area, not too much to do but to explore the world around me on a bicyle. Had a coaster brake on several bikes back then and they never seemed to be able to stop me well or just ended up not working randomly. Good thing kids heal quickly or else my childhood probably would've sucked... Then got upgraded to an antique 3 speed rim brake bicycle, and my life was forever changed at that point.
I don't see coasters as a good mains brake, I'd say leave it on and use especially sparingly. Then install a disk brake on the front, and if possible calipers on the rear, only use the coaster as a last resort should something fail.