i wouldn't use a propane burner (turkey fryer style) in my house, i have used them in my garage and others garages before.
a couple notes:
1. you need to have a window or door open. Fire needs oxygen, fuel source, and a heat source. keeping your doors and windows shut restricts the oxygen that you need for good clean burning. this will result in carbon monoxide. running your car for 10min in your garage will likely create more CO then a propane burner for an hour.
2. boiling water with these burners creates a ton of steam. think about it, your boiling off anywhere from 1-2 gallons and maybe more. this is the main reason i hate to do it in my garage during the winter. you need a good vent to draw that moist air out.
3. they produce a ton of heat so anything synthetic could catch fire if it is too close. carpets, blinds, etc.
now if your working with oil like frying french fries then there is no way i would even thing of doing it indoors. i stay clear of the house or any building in case of a oil spill that catches fire.