I've had some dehydration (or perhaps more accurately, heat stroke) issues, and the solution was to aggressively hydrate (when I run, I wear a fanny pack that holsters a bicycle-style water bottle) and to have Gatorade as part of the mix (usually about 50/50 with water). The extra gunk in Gatorade makes a serious difference.

What I've observed, thanks to a heart rate monitor I use while jogging, is that I have to carefully control my heartrate when running. If I keep it under 170bpm for the whole run, I'll be fine afterward. If I let it creep up into the 180's, I'll be a zombie for hours afterward. That's what actually pushed me to run less and swim more, since the pool represents a giant heat sink. I can push a lot harder at a lower heart rate. Toward that end, you may find that swimming lets you work out without the dehydration issues. (I've seen some hardcore swimmers who also keep a water bottle on the side of the pool, since you do still sweat and you don't particularly want to drink the pool water.)