If the coolant temp gauge reaches operating temp which is about 185-190 deg, this tells me the engine is at working temp range. Loaded or unloaded, the engine is working at the designed range in terms of temperature. If the truck is loaded, the coolant temp would rise but settle back down. So if the coolant temp gauge is used as a measurement of efficiency, then I don't see how loaded and unloaded conditions would affect the decision whether to buy diesel or gas.
I think the term efficiency can be taken in another way. By using diesel, the MPG does not really change too much as compared to gas when driving loaded or unloaded. For gas motors, MPG is dependent too much on the load and its rpm.
I bought my Cummins based on the uncertainty on whether I will have an
RV trailer or not. I didn't want the truck to be the limiting factor on what size RV I can buy. The people I work with who have RVs all told me to get an HD diesel truck. Nothing less. Some tried the 1500 and some tried 2500 with gas but they all said diesel is the way to go. Towing a RV trailer is a difference of 1500 rpm for diesel versus 4000 RPM for gas. I think the only penalty in buying the diesel is the maintenance. 3 gallon of DELO+$15 oil filter+2 fuel water separator gets expensive. The air filter is expensive too. The DEF fluid is not too bad.
I have a RV travel trailer (6000 lbs). When the wife packs up the whole house, it is about 7000 lbs. I realized after a year with the RV travel trailer, I need a bigger one such as a fifth wheeler with slideouts. If I had bought a 1500, it would be a problem.