All three of these are great carriers, but the HaB is definitely the best suited for newborns. It's super comfortable, very versatile, and you'll get a tonne of use out of it. I highly recommend this carrier for any age baby, but I think would be perfect with a little new one snugged up against you!
As for heat... I used a HaB last summer with my then 6-8 month old and didn't find it that bad at all. On the hottest days I try to stay inside in AC, but in truth any time you have a baby up against you it's going to be hot regardless of the carrier or the weather!
You can get the Ergo with an infant insert (which I haven't tried) but I really don't think it would be as comfortable or cosy as a sling/wrap/pouch.
The Kozy can be used with a newborn but again, isn't the best option. This carrier works best after 3 or 4 months.
Magical Mama, joyfully home educating my three wonders: FR (12/02), EG (05/05), DK (06/09)