Locate the master switch connected to your Burnham oil furnace and switch it to the off position to turn off the unit.
Locate the heat sensor rod next to the pilot light assembly. This sensor detects the presence of the pilot flame. If no flame is detected, it will shut off the power. If the rod is dirty or caked with dirt and soot, it may be malfunctioning, causing the unit to randomly shut off.
Remove the screws holding the front panel of your furnace in place and take off the front panel. You can now see various components inside the furnace.
Wipe the burner assembly free of any caked-on grease, grime or dirt.
Replace the front panel and flip the master switch to the on position. Test your furnace once again. If this fails, you can try pressing the reset button located on the unit to reset the system. This may also clear any glitches with the furnace.