It's doable. The speed limit, at least on the northern part, is 50mph, and rangers patrol it regularly. They have nowhere else to go, so they ride up and down all day long. From Natchez, MS to the north end in Nashville is 442 miles so that's right at 9 hours of riding with no stops. Two days would do it easily.
If you are into history there are a lot of stops along the way. I've only been as far south as Tupelo, MS but the main visitor center for the entire parkway is there. There is also Tupelo National Battlefield, and tons of little historic stops every few miles. Colbret's Ferry (just south of the MS / TN border) is a pretty place as is Metal Ford (about mile marker 382 or so).
Keep in mind that there are NO commercial establishments anywhere on the parkway. You will have to get off to find gas, food, whatever. If you are camping there is a campground at the Meriwether Lewis Monument at mile 386, otherwise you'll have to get off the parkway to find a motel.
The northern end at Highway 100 in Nashville is at mile marker 442. As you said, it IS hot. Most of the stops along the way do not have restrooms although there is usually one about every 20 miles or so. Those are going to be the only places right on the parkway to get water so take some with you and stay hydrated. The temperature here has been unseasonably hot with temperatures in the mid 90's and heat indexes a bit over 100.
Scott Craig - Nashville, TN
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Last edited by SCraig; 06-17-2011 at 08:10 PM.