A ventless heater that almost over heats

I live in the northeastern part of the country, where we typically get extremely cold and snowy winters.  Last year, we really didn’t get much of an autumn.  Winter arrived almost on top of summer and stayed all the way until April.  The temperature in February dropped down to twenty below zero and stayed there for over a week.  We were very worried about our pipes bursting, and my husband brought home a portable heater for our basement.  He ran the heater every morning and every night, just long enough to bring the temperature up to freezing.  We also had problems with our heating system in the house.  My kitchen is heated by a small ventless heater, that is normally capable of keeping up with the requirements of that single room.  Last winter, however, the heater ran constantly.  Once the kitchen reached the thermostat setting, the little ventless heater kept right on pumping out hot air.  It was a problem because the unit began to overheat.  I had to manually turn it off and on.  I tried cleaning the filters, but that didn’t help at all.  I finally figured out that there was really cold air leaking in around the natural gas pipe.  The cold air was blowing directly on the heater’s internal thermostat.  It was telling the unit that the air in the kitchen was well below zero, and so the heater would never shut down.  I had never noticed this leak before, and I can’t begin to guess how much it cost me in wasted energy.  Once I sealed up that hole, the ventless heater worked just fine.