Perhaps "thinking about" has a more "considered" air, in your examples; perhaps "thinking of" suggests that the thought has only just occurred to you.
But in practice, with that example, I don't think many native speakers would register a significant difference between those two sentences.
PS: Probably the past tense ("I spoiled") would be better in your post, as another event (my answer) has intervened. (But "I've spoiled" wouldn't be wrong; it simply gives an impression that your focus is still on your question, rather than subsequent events.)
A: We have tried to solve this problem but could not come up with a solution.
Can you suggest something?
B: Well, I can't suggest anything off-hand. I will THINK ABOUT IT and
if I THINK OF SOMETHING (solution) I will let you know.