Sheila,
Heat is your transmissions' worst enemy. Most vehichles can be (or are) equipped with an optional tow package which includes a transmission cooler; among other things. This may be in the form of a cooling coil located inside the bottom of the radiator, or may be a seperate cooling coil located in front of the radiator. Some are a combination of both. Bottom line is that they are well worth having for whatever driving conditions you encounter. Having it installed in front of the regular radiator is best, and does not usually decrease the engine cooling capacity to any noticeable extent. Number of cores, frontal area of the radiator, etc, is not something you normally have any control over - it's something that's designed by the vehicle manufacture for your particular vehicle and the driving conditions it's expected to encounter. In fact, I would challange anyone to tell how many cores are present without physically taking the radiator apart. What you should be doing is watching the temperature gauge on a regular basis when driving up long grades, in hot weather, or high altitudes. When it starts to creep up beyond the normal range, pull off and let everything cool down some; then continue your trip. Maintenance is equally important. Make sure your cooling system is clean, replace and top up the coolant at recommended intervals (as per the manufacturer or as required), check and replace hoses and belts as required, and keep the area in front clean of leaves and other debris. Thermostats are also important. At sea level and normal atmospheric pressure, water boils at 212F. At higher altitudes it will boil at a much lesser temperature, and those bubbles will greatly reduce the cooling efficiency. A good, all around thermostat would be one rated at 190F opening temperature, and is the one normally installed by the manufacturer. Without knowing your GVWR, options, engine size, rear-end ratio, etc., it's difficult to say whether your tow vehicle is up to the task, but perhaps someone who's more familiar with the F-150 can step in and shed more light.