I have personally towed a K-5 with a K-5 on my trailer several times (my trailer is 1,681 lbs empty). I never trust a "bumper hitch" to tow anything, period. Personally, I would put a 2" receiver style, frame-mounted hitch on the M1009, a well-balanced car trailer, and tow the Jeep without giving it a second thought. However, note that I said "well-balanced" trailer, what I mean by this is that when the trailer is loaded, your main spring pack should not be down on the overloads, you want some tongue weight, but not excessive, the trailer should be holding most of the weight. If you have the option, ensure your trailer has brakes on it.
Basically, as far as "structural integrity" of the M1009, which doesn't appear to be rusted out, I wouldn't sweat it. As far as the overheating issue when towing, I wouldn't concern myself as much with this unless you are planning to tow something larger than the M1009 up hill through a Rocky Mountain pass (in that case, I would not do it). The biggest thing I would consider when towing with your M1009 is stopping. You need to ensure you can stop whatever you are towing, because that truck can PULL more than you could ever dream of stopping with it, and further more, because of how short the M1009 is, you need to ensure that you are not going to end up with "the cart in front of the horse" if you have to lock down on the brakes in an emergency.
As a general rule of thumb, I try not to tow anything that is more than 150% of the overall length of my tow vehicle, and I try to keep my load to the equivalent of whatever I am towing with + my trailer (e.g. if pulling with an M1009, then nothing larger than the M1009 on my trailer... if I am pulling with my dually, then nothing much larger than my dually on the trailer... usually). And this is all contingent on several other factors that are unique to every situation, such as how far are you towing? What are the conditions of the road, your equipment, the weather? Is there an alternative? How many hills are on the route? Can you re-route? What does your insurance company say, are you covered with the load you intend to pull? Have you made intentional, quality upgrades to your truck for the specific purpose of aiding in carrying a load? Do you have brakes on the trailer? Is your vehicle licensed to carry the load you intend to pull, weight-wise? Etc. This is just my input, ultimately you are responsible for your own actions in the end. And just because I have done something in the past just demonstrates that it CAN be done, not that is SHOULD be done again.