I'm not sure exactly what a thermo-dynamic engineer does, but the USAP needs engineers, and my understanding is that a good engineer has a good chance of being hired on - if you have the skills they need.
It's a bit late to apply for the coming summer season, but it's still a possibility if you act fast. It will take some time for medical qualifications and all.
You're unlikely to be washing dishes - that's a separate duty at McMurdo, and combined with janitorial duties at South Pole. For the other stuff, you'd have to be a General Assistant, a UT, a plumber, or working in waste - and I think I still missed a category - but none of those would have all of those duties. Keep in mind, during the summer McMurdo has roughly 1200 inhabitants. There's a lot of specialization there. South Pole, with about 250, has less, and Palmer, with less than 100, I think has the least specialization.
In any case, if you are really interested go meet some people in Denver. You might even have a chance at a full-time job that happens to require you to go to Antarctica for a few months each year.
Anyway, welcome to the forum and good luck.