You can add a transaxle cooler to your car. We have been towing our light weight
trailer for 11 years.
Car came with 7 pin wiring, electric brake module, hitch and extra safety systems from the dealer. Dealer wanted all of this to pull the trailer and have our warranty at the time.
Check out the little unit from Mr. Transmission it is said to be a progressive cooling unit that will not over cool the transaxle, trailer centers can add the brake module and 7 pin wiring for you, Get a good hitch with sway bar; We had our original Hitch customized by a specialist Andy Thompson at Can-AmRV in Sarnia Ontario.
The custom frame hitch is made for a unibody car and fastens both at back of car pipe runs forward to bracket at split seat reinforcement area of car. We use a Weight
Distribution Hitch (WD) they make them for light weight
trailer units as well as large trailers.
Our Trailer meets the class I weight limits empty but its size means we need a class II in Ontario and they do not make a class II that fits a WD unit. "boler recommends class II with WD in original documentation" it is also posted on inside of closet door. We upgraded to a custom class III frame hitch as we have a unibody car. We were told by dealer that 8% to 9% should be on the tongue; we are a little light but it travels very well.
Hitch needs to be as high on car as possible or you may drag ground with ball when not hooked up at some of the more extreme driveway exits.
Hope this is of help.
P.S. we also upgraded the Toyota wiring module in trunk to one with a dedicated power wire for the trailer battery
from trailer dealer. Toyota unit overheated and caught fire on our second or third trip luckily we had a fire extinguisher in trunk of car at the time.
Toyota was going to add a replacement module under warranty but we did not have them replace their unit with a new one as it was a known problem online at the time instead had a heavy duty unit installed.
Andy Thompson was on the committee that set the current rules for towing He really knows his stuff.
I am not a specialist but was told that all trailers with 1000 lbs or more require electric brakes
; do know that in Ontario it is 3500 lbs or 50% of the weight of the towing vehicle or more and electric brakes