Chosen Solution
iPhone 6 with broken screen changed for new screen and now hot home button, changed for another screen and back plate but still the same hot button issue. All connections triple checked. Only thing that may have effected it, the LCD including the home button from this phone was momentarily plugged into an other phone, iPhone 6s Plus, to test the screen before being fitted. Yes I now know that probably not a great idea in terms of potentially bricking the 6s Plus, (it didn’t) but why would it cause a problem with the physical iPhone 6 home button now getting hot?? I know that the battery is bigger but is a 6s plus different operating voltage? is the button burned out or something?
The buttons are not compatible. I don’t have the schematics but it is possible that the voltage or even the wiring is different. However since you plugged it in an iPhone 6s Plus, the button should not be affected. It is likely that you tore or shorted something in the button during disassembly.