When I used my Immersion chiller, it came with clear vinyl tubing. The "inlet" one has a garden hose adapter at the end of it and nothing out the "outlet" side. I don't recall ever having an issue with it regarding heat, in fact the outlet side of the vinyl tube wasn't even clamp onto the coil, it was just wedged on and never had a problem. The tubing was clamped to the coil on the inlet side though.
If you need to purchase tubing, co for the vinyl braided one one because it will last longer IMHO. If it came with Clear vinyl tubing, just use that.