You probalby have a toilet mixing valve or tempering valve that has failed, to hot.
The toilet that runs ocasionally probalby is leaking, put some food dye in the tank and it will probalby show in the bowl.
This is a example of mixing valve, this one is adjustable http://www.albrightshardware.com/depart ... 4-mpt.html
This link is broken, either the page no longer exists or there is some other issue like a typo.
Mixing vavles are installed to prevent sweating toilets, and help keep the drainfield form freezing, for the latter I would close a valve in the hot water for the summer.