It's working a lot harder when you're pulling a trailer, so it will always run hotter. If it's overheating, you might be pulling more than it's rated for. Otherweise, check your coolant system. If you haven't flushed it out in a few years, it's probably time.
Beyond the fact that the engine is working harder most of the 97-2004 f-150's use a small transmission cooler in conjunction with a system that runs transmission fluid through the radiator to cool it. When towing the transmission fluid gets VERY hot when shifting gears. Make sure you have the overdrive switched off to prevent unnecessary shifting. If you plan on doing a lot of towing it is highly recommended to add a large external transmission cooler. You can still have the fluid run through the radiator if you'd like or you can separate the systems all together. If you choose to separate the systems all together you need to add a transmission temperature gauge as the only warning that the transmission is overheating in the current configuration is that the radiator gets too hot.
Hope this helps.
How do you rent a hunting dog?
You can try to look in classified ads in your area for hunting dogs to rent. Some online sites such as Craigslist may have rental dogs available.