Is it safe to leave a portable heater on overnight?

My friend bought a small portable heater (it was like $10.00) and it uses a fan to circulate the heat into the room. I was thinking about getting one as well since for some reason my room is always the coldest in the house. Is it safe to leave them running over night while sleeping? I know some have features to turn off at a certain temperature. Any advice on this? Are they bad for the electric bill?