Tealeaf, you definitely continue to burn more calories after strenuous exercise.

It's called EPOC -
excess
post-exercise
oxygen
consumption. So you're right, a good exercise session will keep your metabolism running high for hours afterwards.
Did you know that you get the highest EPOC with interval training? That's when you add in high intensity bursts to moderate intensity exercise. It's like adding in 1 minute sprints when you're jogging or cranking up the resistance on the elliptical for a minute or two, then dropping back and recovering. I think the steep hills on your walk are your intervals and I bet your heart rate is really high when you reach the top!!
When I said that muscle is the only way I know to increase your metabolism, I was only thinking of resting metabolism. Thanks for pointing out that exercise also temporarily increases metabolism too.
The big advantage of adding muscle is that you're burning more calories 24 hours a day, 7 days a week, awake or asleep. And that really can add up! I like the idea of my muscles doing the work for me, even sitting here at the computer.