I am talking about two very different types of heaters, the forced air ones are the ones usually used at construction sights are NOT to be used at home unless you really really have to, they will kill you in an unvented room.
The traditional kerosene heater that I have used for several decades has a round wick that draws up kerosene and basically burns like a clean candle, you adjust the flame to the point their is almost no yellow, they can be used indoors but still require some air movement, these I MIGHT use number 1 diesel in a pinch, would stink like well a diesel truck. Yes they could work on number 1 but number 2 diesel would smoke too much, not as light as number 1 diesel. Best to get high quality kerosene fuel and add some additives to remove any other smells, plus to remove any moisture from stored fuel.
Seeing as my heater is just for emergencies that is what I do. Here in the Seattle area when we get power outages there are ALWAYS two types of stories. One where the generator is brought inside (or the garage) and people get sick and/or die. The other is people bringing their charcoal Weber grill inside to keep warm - Asians mostly. They don't realize it isn't the same type of “charcoal”, and also the homes are more weather-tight.