Once the solvent evaporates, the only source of odor or gases would be the plastic resin in the paint getting hot enough to cook.
The outer shell of the heater isn't a problem, and if you were careful to not get paint on the heating element, you have nothing to worry about. Be aware that when the heater is hot, it may initially expel some more solvent from deep in the paint that normally evaporates too slowly to smell. But this will be temporary.
If you got paint on the heating element inside, the result will depend on the type of element. If the internal heating element is a pipe of hot water or hot oil, that won't get hot enough to cook the paint (although you might get some initial odor like from the shell). Those elements often rely on metal fins to radiate the heat, and a lot of paint on the fins may cut down a little on the efficiency.
If the heating element is a metal ribbon that gets hot, that will char any paint you got on it. It will stink (and may smoke or ignite), and those vapors won't be good for you. But that will happen within the first minutes of use, leave some charred paint on the ribbon, and be done; it won't be a continuing problem. If any paint does burn, that should be contained within the heater. But you might want to move anything flammable away from the heater when you turn it on for the first time as a common sense precaution.