SweetLou, Glad to know you will be getting new tires. When you said that you were not overloaded because the trailer was matched to the boat, you neglected the most important factor, the tires. I don't care what the boat/trailer combination is, the tires are the most important factor here.
To do this right, weight the boat/trailer combination. Find tires that will cover this weight and put them on. Most small trailers come from the factory with tires that just barely cover the gross weight of the trailer. In such cases it is imperative to air up the tire to the max pressure allowed. If 35 is the max and you run them at 30 you probably are underinflated for your weight. Underinflation causes excessive flexing of the tire which produces the heat you felt. Let alone this heat will ruin a tire. It is a falacy to think under inflating a tire will somehow protect it in the heat. Exactly the opposite happens.
I run LRE tires with a max inflation of 80PSI. I run 70 PSI because at this pressure I am still way above the weight of my trailer. On hot trip I will inflate to 75. If it is extremely hot, I will run 80.