Getting that kind of analysis as part of a so called free estimate is pretty tough. You might be able to find a contractor desperate enough. But just as likely you may find that only a minority even can do a real heat load calc. Most use rules of thumb and goofball short forms. Of those that do the real deal, I'll be surprised if they'll do it for free. At best they might do a quick whole house heat load calc.
If they hand over a calc see if you can find out how it was produced. A simple one page form with blanks filled in, or anything like that, isn't a Manual J heat load calc.