I don’t think the material will make much difference in heating/cooling. The material would be pretty thin so not much thermal mass. Plus the mug is an insulator.
One thing to consider is that not everyone uses a mug like that. I think more common would be a take out starbucks cup, so you need to be able to get it out without a handle.
You latest concepts look a bit more interesting, but honestly I can’t really see that point of the whole thing. Is your company really going to tool up and go to market with this? You said it’s not just an exercise, right? Have you questioned the original premise that this product is even wanted/needed? Might there be a better product with same/different materials that is more interesting and has a better opportunity in the market?
R