I have taken Liam out in public places, such as the mall, vets office, supermarkets, etc. I'll usually wear a sweatshirt that has a big pocket and he'll sleep the whole time in there. As I live in South Florida, temperature isn't a problem for me, because trust me even when it's cold, it's hot.
I would however advise not to bring your future baby out if you live in a colder region where you know you won't be able to keep them warm. Other than that I'd say go for it because as far as people go I never actually flaunt him. So 98% of the time no one notices I have him with me lol.