Technically, you cannot extend your Schengen visa anywhere else than within the Schengen area but extending a visa is only possible in very specific situations (e.g. you are stuck in a hospital). So in your case, you will actually need to apply for a renewal/new visa (and that is generally not possible from within the area).
Generally speaking, you should apply for a visa from the relevant consulate serving your current place of residence – and nowhere else, not even another consulate in the same country – but there are some limited exceptions. For example, if you have good reasons (say documented professional or familial obligations) that force you to be out of the country for a long period of time before your next trip to the Schengen area, you could try to convince another consulate to consider your application. But mere convenience or a holiday in Thailand would not be enough typically.
See the following questions for details about that:
But in your case, it's important to note that there is no special significance to the date of expiry of your current visa. You can in fact apply for your next visa before that and the consulate will simply issue a visa starting some time after the end of your current visa (either directly after it or at the date of your next planned trip). If you did not have a multiple-entry visa, you would only be allowed to apply during the three months prior to the next trip but when renewing a multiple-entry visa, it's at any time during the six months before the expiry of the current visa, cf. article 9(1) of the Schengen Visa code.
This means that you have a great deal of flexibility and it doesn't matter whether you are out of the country during the month during which your visa expires or immediately before the trip. That's not impediment and also would not be a good reason for a consulate to make an exception because you can actually apply at any time between between now and February.