How to deal with a student found seeking an answer to a coursework question online?
Identify the offline equivalent of the observed behavior, and then act as you would normally. Remember, that the burden of proof for academic dishonesty likely resides with you. This includes verifying that the poster is indeed the student you accuse.

I find this situation to be pretty common: https://chemistry.stackexchange.com/questions/2753/how-to-derive-partial-gas-equation. Most stackexchanges have a homework policy. I would consider homework questions posted to stackexchanges to be no worse than asking students who have taken the course before you or asking another professor. How you deal with it is up to you.

What would your response be if you saw a student collaborating on the problem in a study group? How do you respond if you find out that your student asked another instructor or a grad student in your department for help? If you learn the student worked on that problem with his/her tutor? If the student looked up the answer in the textbook or the solutions manual? All of these are common and to varying degrees accepted (if not liked). 

I would guess your irritation over this is somewhere more than the student asking one of your colleagues (who being nice will actually do the problem) and somewhat less than the student stealing another student's answer. Identify the offline equivalent, and then behave as you would normally. 

EDIT - I missed the last part of the question. 


  I have a good idea who the student is, but no definitive proof. How would you handle this situation?


If you do not have proof, then suck it up and let it go - this time. Next time put something in your syllabus. Either write a pretty severe sounding policy that exists to deter the behavior (because your policy will be basically unenforceable), or write harder questions and encourage them to use online forums with the caveat that they document all of their interaction. The second option shifts the burden of good behavior to your students.