Meaning of sentence with double negation

I'm a learner of English, and I got this sentence from a dating book which I find difficult to understand:

We know a man who was horribly disfigured by fire who has a constant stream of women in his life, who would never dream of thinking of himself as sexually inadequate.

The word never is a negative word and inadequate also has a negative meaning. There are two ways I can understand this sentence:

(1) Negative plus negative gives positive (my Chinese grammar), so the sentence means the same as

He would dream of thinking of himself as sexually adequate.

(2) Double negative strengthens the negation, so the sentence means the same as

He would dream of thinking of himself as sexually inadequate

or

He would never dream of thinking of himself as sexually adequate.

Your option #1 is much closer to the intended meaning, but you haven't quite construed it correctly. The two negatives do indeed cancel each other out. But when you cancel out the word never the result is always, so the plain un-negated sentence would be something like

He always dreams of thinking of himself as sexually adequate.

However, this still misrepresents the meaning. This is because the idiom to never dream of carries a negative connotation, and when you un-negate the sentence you should take out that idiom entirely. So the plain meaning of the sentence is more like the following:

He always thinks of himself as sexually adequate.

Or, to put it more strongly:

He is confident in his sexual adequacy.

Neither of your proposed interpretations are correct.

In this case the the negatives cancel each other out to make a strong positive statement. When you filter out the prose the meaning is something like this:

He knows he is sexually adequate.

If you would "never dream" something, you know that the opposite is true. You don't have to dream about it being different, you just know. If you would "never dream" about a negative thing it means the positive thing is quite certain in your mind.