The heater in my Bunn Coffee Maker continues to heat. It got so hot this morning the top of the coffee maker began to expand

Most probably the relay that drives both the heating element and the warmer.

A black thing like little box (relay)that containes 8-6 wires (2 from main board and rest just go other components.)
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The manual for this coffee maker can be found at this link:
http://manualheaven.com/assets/bunn-nhbx-b-contemporary-coffee-maker-manual.pdf
While the manual does not contain repair instructions, it does have some troubleshooting tips to follow if your coffee is not staying hot.

Contact the manufacturer directly at:

http://www.bunnathome.com/parts-service

While this brewer does have a reservoir that keeps a couple of pots worth of water hot for brewing you can get a cooler second pot if you brew directly after. You should hear the brewer heating up after brewing. Try waiting until it is back to temperature before re-brewing. If that heating takes more than a few (3-4) minutes then you probably have a problem with the heating element and the water is only being heated by the "keep warm" heater.

The Bunn coffee maker does not operate as most coffee makes do. You cannot leave the Bunn in the off position and then just flip the switch to on and pour the water in. You will always get cold coffee if you do this. It takes time for it to heat the water. The On/Off switch should be left in the On position all the time. This keeps the water hot in the tank, thus providing hot water when you need to make coffee. You then just pour the cold water in the top, shut the lid, and have a pot of coffee in 3 minutes. The On/Off switch is a vacation switch, and you use it only when you are not going to use the coffee maker for a couple of days. Older Bunn coffee makers did not even have an On/Off button. You simply unplugged them when going on vacation. So turn the switch to the On position and leave it there. The unit will then work as designed. Forget how other coffee makers work, this is a Bunn and it is the fastest coffee maker you can buy and must be left on all the time. that way the water stays hot and the unit will keep it that way.

Most likely suspect is the thermostat, however you might want to check the limit switch also(located on boiler between elements).

before plugging in place your empty filter basket in the coffee maker and place a pot under it. Slowly pour in two pots of water using the pour pitcher. Now you can plug it in. it'll take 15 min to heat up first time . when you brew your first pot leave your water level a little short,because the water will expand (only the first time)

This sounds like a short in the main heating element. If you are within your 3 year warranty, Phone Bunn and talk to their warranty department. They will give you a RMA number and give you further instructions. If not, there are no replacement parts available for these brewers.