Any extra cooling you can have for the motor or trans is only going to help.
My question(s) about going with a mid sized vehicle like that: With about 800lbs for payload in the trailer (what is the yellow sticker in the trailer state dry weight with propane is?) and you are planning some longer trips, will you have the available payload for the required amount of clothes, food, and needed items? I understand at some point you will need to do some shopping for food and necessities, just wondering? And IF the trailer doesn't have enough payload for such trips, will the vehicle handle the overflow of goods?
Also, with a gvwr of about 3700lbs for the trailer, loaded at say 3500lbs (rough estimate) you could have a tw (tongue weight) of about 420lbs- 520lbs (12-15% of loaded trailer) depending on what your trailer likes for a stable tow. Some trailers need less tw, others like more tw. So as mentioned, make sure the yellow sticker in the drivers door jamb that states "All passengers and cargo not to exceed xxx(x)lbs.... is enough for the weight of all passengers, cooler(s), gear, ~100lbs for the wd hitch, and the estimated tw. Also check the receiver hitch for the max tw rating, and trailer weight to be sure you are good to go.
As for keeping the speed down, it is the best when pulling a rolling brick down the road due to higher center of gravity, stopping distance increasing, etc. But if you are so inclined, you could always swap the tires to a set of Carlisle RH's which have a higher speed rating than 65mph for the extra "cushion" between travelled speed and the tire's speed rating. We have had good luck with them the last couple yrs on our last trailer. The new 32 BHDS will get a set of RH's (or maybe the new model tire they are supposed to release) in the Spring.
I do not suggest you can fly down the road if you buy a new set of tires, just the peace of mind driving at about 65(ish) mph on a set of tires rated at 65mph, or a set rated for 81mph. Same as if possible, stepping up the weight rating of the tire for more reserve capacity which I will be doing as well, LR E from a LR D.
Good luck!