Is it appropriate to ask one of my thesis-committee members for a postdoc position? I'm about to give submit my Ph.D. thesis to my selected reviewers. Among the external reviewers, I really like the research themes that one of them is working on. So, I want to ask him about any possibility of working in his lab as a postdoc by sending him my CV and a proper statement of interest in the specific research topic(s) he works on.

However, he is going to read my thesis during the next 3 months, and I'm not sure if my request is going to have an effect on that process or vice versa.

Also, I cannot wait for 3-5 months to see his feedback on my work (and the disputation outcome) before asking him about the position as it will be too late for me. So, either I should ask him now or not asking him at all! :D
I don't see any reason not to ask. I think that any "conflict" because he will review your dissertation would be minor. A post-doc position is a two-way affair in which you both give and get, so it isn't like pandering on the one hand or asking a favor on the other. 

If your general relationship with the person is good, and you want to work in that area, then yes, ask. But be sure, before you ask, that you wouldn't be rejected out of hand. You need at least to know that you would get serious consideration even if you aren't accepted. An informal explorative meeting might be one way to broach the subject, followed up with a more formal (CV, SOP, ...) application. 

On the other hand, there is also something to be gained from working at a different institution, with new colleagues and new ideas. Don't neglect to look for alternatives in other places. 

But also note that this answer may not apply universally. My experience is in the US in mathematics and CS.