Q: Home button hot, any ideas please

Hi there Paul,

It sounds like your Home button is actually giving off heat, and your battery life is very short. Right off the bat that indicates to me that you have a hardware issue and I would recommend setting up service:

iPhone Repair - Other Repairs

You could if you like, troubleshoot the software by backing up to iTunes and restoring the phone as new to see if the issue persists:
 
How to erase your iOS device and then set it up as a new device or restore it from backups
 

If it works as expected when set up as new, then restore your backup to either verify it still works and the software just needed reinstalled, or isolate the issue to the backup file itself. 

Thank you for using Apple Support Communities, all the best!