I've had sims survive an "execution by fire" before. Unfortunately, it's not 100% foolproof.
The easiest and cheapest way to maximize your chances are to build a 2x3 room, place the bottom of the line fireplace in it, drop in a 2x3 rug and add a door ("moveobjects on" is required to do all this). Send your victim in to light the fireplace and remove the door. You don't really have to do anything else after that, because as long as the fireplace is going, they'll poke the fire autonomously since it's the only thing for them to do. However, cuing up "Poke Fire" interactions seems to speed up the process.
Eventually the rug will catch on fire, and they'll have nowhere to go to avoid the inferno.