From the UK, I did it online - you need a crime reference number (which can be reported/obtained online), or I guess in your case, evidence that you've reported it to the Police. The application form needs a lot of stupid (sometimes impossible) questions answered eg when were your parents married? If like mine, your parents are dead, you'll probably have to do a lot of research.
Obviously, it will cost you the same as the original.
When you find out how to do it properly from Thailand, please report it here, as I doubt whether you're the first or the last - it could be a valuable resource.
You can get temporary travel documents from the Embassy in Bangkok apply in the morning and you should be able to collect in the afternoon they do however need a police report.