Helene,
Sorry you encountered our heat! It can be brutal so we ride early in mornings. As for the Memphis bike trails - downtown can get a little sketchy if you are unfamiliar with areas; but, if you were to drive east to Shelby Farms, or the Wolf River Conservancy trails, there are safe places to park and you can ride lovely trails integrated with Shelby Farms (under reno). 2016 will bring a new revamped lake at Shelby Farms, and additional miles along both the Memphis Greenline trail and the Wolf River Conservancy trails into Germantown and Collierville. We hope to be able to complete 35-40 miles in a round trip on the trails.
AngelontheRoad