Assuming your closet has 8' ceilings, you'd have about 1.33 watts per cubic foot so that should be more than enough.
For small rooms I have had very good luck with those oil-filled, radiator style space heaters. I had a 7x7 room in my last garage that was not insulated and had two exterior walls. The door to the room was hollow-core and opened to my unheated garage. In South Dakota, no less. I just stapled Reflectix to the walls and ceilings and was able to heat the room to the low/mid 80's with one of those space heaters. I did not even have to turn it to it's highest setting.
So one of those could easily handle your closet.
If you really want to make it efficient you could staple Reflectix to the walls, ceiling and doors. Here is a picture of that snake room I had in my last house. I had not yet covered the ceiling with Reflectix when I took this picture.

You'll be amazed at how little radiant heat will be required to heat your closet.
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Current snakes:
0.0.1 Gonyosoma oxycephala - Java locale (green)
2.2 Gonyosoma janseni - Seleyar locale (all black)