Has there been a change???? I always said a lot of thanks but am hearing more and more often 'much thanks'....as well as other similar instances of countable and non countables...
Thing is, it depends on the context of the phrase. You might hear "A lot of thanks are due to him" or "She congratulated him with much thanks"... although they both sound wrong to me. It depends, as bluedolphin suggested, if "thanks" are something you can count or not. But as Jaybee says, I think "many thanks" would be better in all situations.