A light rail is coming to Austin. Existing tracks have been purchased and now stations and commuter trains are to be added soon. There are a lot of bike lanes, however, you are correct that the city is designed for cars.

As for the extreme heat, it helps if you don't fluctuate between air conditioning and the outdoors. If you are going to be outside all day, stay outside. Wear loose fitting, light clothing and always have something to drink with you. Shade is also your friend. You do adjust after awhile.