You lube the rubber bush the caliper mounts to it's carrier through. This allows it to slide left and right a little bit as you use it (right when you apply the brake, left when you release it). So yes, lack of lube there may be your issue. When it gets really hot it may be hanging, sticking and not moving as it should. There's only one bolt and rubber bush that holds the caliper to it's bracket, the one with the yellow paint on it here .....
View attachment 250743
You can kind of test it by grabbing the caliper and seeing if you can move it in and out a little bit, check to see if it's sliding in the rubber bush as it should.