I used a 2000 Mercury Mountaineer (Explorer twin) with 5L V8 to tow a 23' Rockwood TT with slide. Dry weight was about 3400 lb. With overdrive locked out it did the job ok, but just ok. I did not drive over 60 mph, and of course when headed up long grades I would shift down and slow down even further. Typically I'd get 18 mph highway, but 10 mpg towing. Hit a headwind and that went down to 8.5 or 9 mpg. Ugh. I still have that Mountaineer; my wife won't let go of it, so it's her around-town vehicle.
I think you'd be ok with that rig, so long as you don't want to win any speed awards. Keep it under 60. Make sure you have adequate cooling for the tranny, like you say. Maybe get a Scangauge and plug it into the OBD port under the dash so you can monitor your transmission temp. For that rig I would suggest a look at the Anderson No-Sway hitch; I used one to tow a 16' TT with my Highlander last summer (5000+ miles) and it worked very well, was easy to hook/unhook and has no bars to stow away while unhooked.
