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As requested, here you have a couple of quotations that give a satisfactory explanation on the topic above:

Re: Think of vs Think about

To me, think of is stative-like and means to hold in your mind, whereas think about is active-like and means to consider.
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Basically, 'think of' usually means 'imagine' whereas 'think about' tends to mean something closer to 'consider', so the differences would arise in certain contexts. For example, if I say I'm thinking of a tropical beach, please don't interrupt me! I mean I'm imagining it or daydreaming about it. However, a sentence like 'they're thinking about whether to agree to the sale,' means they're considering the sale. In these cases, it's just natural usage patterns that tend to favour one form over another

But when we are talking about people, we often tend to use them both in a similar way: For example, if my friend had an accident and went to hospital, I might send a card and some flowers with a message which could either read: 'I'm thinking of you,' or 'I'm thinking about you', and the meaning wouldn't be significantly different.