There's a LEGAL answer and a practical answer. Like the Thai's say, "Up tp you".
For practical purposes you can work on-line while in Thailand. And you can probably get away with it without a problem.
But LEGALLY the law is quite clear... if you work in Thailand ... even if you make NO PROFIT from that work...you need a non B visa and a work permit to do that.
I'm not saying it makes sense...just that in fact is the way it is.
I'm not sure about simply answering email, but if you are the "boss" in your foriegn company...and you give on-line instructions to anyone regarding what they should do over the net...ESPECIALLY to an employee or associate of yours... you are WORKING under Thai law. And for that you need a work permit and a non B visa.
So, considering that, be VERY careful about what you do on-line and who you tell about it while you are in Thailand.
I'm not trying to tell you what to do, just trying to let you know the facts before you jump into something.
Be careful, and if you decide to do something like that, keep it quiet.