As has been said above, all electric heaters are nearly 100% efficient. The pilot light (if it has one) draws some amount of electricity without producing much heat, but that’s hardly worth talking about. If the unit uses a fan to blow the air around, and it’s a big, powerful fan, this might actually make some minor difference. And as Joe Mahma said, some heater elements do emit some light too.
As for what the heater will cost to operate, you’ll need to know how many watts it consumes, your power company’s kilowatt-hour rate, and the heater’s “on” time. The thermostat can only do two things: turn the element on or off. Depending on how cold your room is, and how high you’ve set the thermostat, the heater may actually be on 20% of the time, 100% of the time, or anywhere in between. Some heater packages have printed cost estimates; I have no idea how accurate they are.
And I agree with what billy said above, about comparing the cost of heating your study room with the electric heater, versus using your apartment’s main heater. We’d need to know how big your apartment is, how efficient its heater is, what type of energy the heater uses, and so on. But I’d still wager that you’re going to save money by using even a costly-to-operate heater in just that one room.
You also mentioned that you’re usually under a blanket at your desk, and your hands and feet get chilly. You’ll notice that most electric heaters are in the 1000-1500 watt range. On the other hand, my twin-size Sunbeam electric blanket consumes just 180 watts. Maybe you could get one of those, drape it down to the floor, and then kinda tuck your feet into it. Or get some slippers. I don’t know what to do for your hands, though.
Some heaters also have multiple elements. For example, you might have one 500- and one 100-watt element; by switching one, or the other, or both, you have three levels of heat (and power consumption.)
Perhaps you could get a small, cube-style heater that you could place on your desk, at its lowest setting, to keep your hands and arms warm. Combine that with an electric blanket, and for just 680 watts, you should be plenty comfy.