You want to maintain at least a 10-15*F temp differential, so a 75*F room should get roughly 60*F water.
My advice would be to bury the tubing in a trench to keep it underground (rent a trencher to get it a few feet deep at least) and then backfill it. Tubing sitting on the surface would indeed get too warm and would be prone to more damage. If you have gophers make sure your lines are chew-proof, I think they make an aluminum-sleeved- PEX line now that oughtta work but I'd do some homework on it to be safe.
The piping you're talking is called Kitec. It's not made anymore because of all the lawsuits and problem's it caused after end user's installed it.
You can buy triple lined pex piping @ Home Depot. It's red in color, and has some special anti-corrosive lining in it. It's specifically made for hydronic applications.
To have any kind of cooling effect, you're water has to be 20F colder than your ambient room temp.