I have a 2015 MBP too and it was struggling when connected to my 4K external monitor. I have written about it in this post. Opening the lower case and cleaning the insides out with a can of compressed air should help with the heat. If that isn’t sufficient then you can try replacing the thermal paste. I just did so yesterday (using ARCTIC MX-4) and am happy to report that it has made a difference!
The Mac is able to drive the external monitor now, which it couldn’t earlier, although the fans do run at around the 6,000 rpm mark in order to keep the temperature below 70°C. The AC in my room has conked out and it is pretty hot (around 95°) and humid where I am so that might be contributing to the increased fan speeds too.
Good luck!