You think of something if you try to come up with something. You might make an "effort" to do so, it is deliberate. For example: Think of a title to your essay You think something up if you come across an idea of yours that occurred to you kind of by chance. You didn´t make an effort, it was spontaneous. At least, I was made to understand it like that. I hope this helps. Ask a native English speaker about this, anyway.

I would use THINK UP in the meaning of to invent or develop something spontaneously, like think up a new back-up plan. Whereas, THINK OF means to remember and consider something. For instance, think of some examples.