Towing Issues: towing with a chevy silverado, chevy silverado, duty shocks

Question
i want to tow with my 2009 chevy silverardo 1500. it has a 5.3 liter engine  and an automatic 4 speed tranny and has a class 3 factory trailer hitch. i am towing a 2006 ford escape   with a uhaul tow dolly the ford escape is front wheel drive and i believe it weights 3500 lbs. i want to tow this car 300 miles cross country. do i need an auxiliary transmission cooler for such a long distance?  and should i get some heavy duty shocks on my truck too?

Answer
I don't know the terrain, specs and all options which could make some difference. Generally speaking, I don't foresee any problems as long as it's flat lands without major hills and mountains. I believe those trucks have a tow haul button which will change the shift points and increase transmission line pressure. That will help while towing especially without an additional cooler. Adding a cooler will help but don't believe it's necessary as long as you don't load up the truck or escape with additional weight or travel in mountain country. Shocks are dampeners and will not increase carrying capacity unless you are referring to coil over shocks. I don't see the need changing shocks. Good luck and any other questions just ask.