During ascents while towing, why is it the oil temp climbs so quickly while the coolant doesn't? Where is the oil scavenging all the engine heat from under a heavy load?
How does this affect the transmission temps? I don't understand how the transmission comes into play between the oil and coolant interaction.
Sorry, I don't have all the answers. Certainly the heat transfer issues involved are pretty simple, but in order for answers to be good guesses, the questions need to be pretty precise, and the conditions the symptoms were observed in, carefully controlled.
The coolant system has some ability to regulate it's temperature, but the oil system doesn't have that ability to add heat xfer capacity if conditions warrant. So under different demand, ambient temp, and air flow velocity conditions, load vs. temp behavior of the two systems is sure to be different. One can make pretty good predictions as to how the two systems will react differently to different conditions by looking at the heat xfer mechanisms.
The coolant system. Two factors dominate the coolant system's ability to dump more heat if needed. The first is the thermostat. As the engine produces more heat, the thermostat opens up more, so more coolant flow goes to the radiator. The more hot water to the rad, the more heat energy is dumped. This ability to increase heat xfer maxes out when the tstat is fully opened. At that point, much of the coolant system's ability to "add capacity" ends. This produces a significant "knee" in the graph of heat produced vs. ability to dump heat.
The 2nd issue is vehicle speed. With the exception of a steep hill pulling a heavy trailer, higher engine loads produce higher velocities. So the additional heat produced by the higher engine load is offset, to some degree, but the increased amount of airflow thru the radiator. That allows the radiator to dump more heat energy. The heat loss effect of vehicle speed is not as significant as thermostat opening because the size of the thermostat opening can vary a lot whereas the speed difference between towing at 60mph vs. 70mph, for example, isn't much.
The 3rd variable that has to be accounted for is ambient temp. Heat xfer is proportional to the temp difference. A 220 deg rad will dump about a 1/3rd more heat if the ambient temp is 40deg than if it is 100deg.
Cooling the oil. The oil has almost no ability to cool itself, excepting the heat radiating from the block itself. But we ignored that heat loss from the surfaces of the hot block for the coolant system, so we should ignore that for the oiling system. The oil/water heat xfer device on the engine block, erroneously referred to as an oil cooler, is fine for warming up the oil under cold conditions, but it's not going to do much at operating temps because there's just not enough temp delta between 225def coolant and 240deg oil, nor surface area, for significant thermal energy xfer.
You asked why oil gets hot. Well, it's because it spends time in hot places. The top half of the block is filled with coolant. The bottom half of the block can get pretty hot tho because there's no water jacket down there. The very top of the head can also get pretty hot because even tho there's water flowing over the combustion chambers, there's enough hot metal up there in contact with the combustion chamber that getting pretty hot is inevitable. And certainly the crank bearings eventually get warmed up by the connecting rods. So altho oil is not going thru voids expressly designed to cool the block, since the whole block reaches a pretty high operating temp, the oil eventually gets pretty hot. It just takes a while.
Re. Why is the oil scavanging all the engine heat when the engine is under heavy load? It's not. Don't confuse temperature with xfer of heat energy. The oil gets hot because some of the places it goes to is far away from the block's water jacket. But the fact that it's hot doesn't mean that it's xferring a lot of thermal energy, nor participating much in keeping the engine cool. Remember that oil doesn't xfer heat very well and with no oil cooler there's no way to dump that heat. Those that have an aftermarket oil cooler will dump a little heat out of it, enough to lower peak oil temps, but if they think they're xferring significant heat energy out of their engine, they're fooling themselves. Lousy heat xfer coefficient and low flow rate.
I mentioned earlier in this thread that at one point I had temp sensors before and after a big oil cooler in the race car. I also experimented with removing the oil cooler all together. I found that oil temps got really hot. Because even tho the oil cooler didn't drop the temp of the oil much due to oil being reluctant to xfer heat, the oil cooler did dump heat faster than the oil was absorbing thermal energy from the engine. That was the example I stated where the oil cooler seemed to dump as much as 2.5deg of heat, yet over time it added up because the engine was adding less with each circuit of oil thru the whole system. The difference in oil temp peaks were as much as 50deg. That is to say, the steady state in a Summer race might be 50deg cooler oil with the oil cooler. Pretty surprising since the oil was exiting the oil cooler only out 2 to 2.5deg cooler. The lesson there was that even tho oil cooler's don't pull much heat from the oil, they do result in dramatically cooler oil. If that seems a contradiction, pls go back and read this paragraph more carefully.
Another lesson I learned in those experiments was that keeping the engine cool had a big impact on oil temps. By putting in a bigger radiator, I was able to drop the coolant temp from 200deg(ish) to 190. My oil temps dropped a similar amount.
A word about thermostats. A cooler thermostat only changes the temp that coolant starts flowing. It doesn't create magic that increases the coolant system's ability to dump heat energy. So if my car's thermostat was fully open at 190, which is realistic, then the larger radiator dumped enough additional heat that the steady state temp dropped 10deg. But it couldn't drop much more because the tstat would have just throttled back flow.
If I had put in a colder thermostat, that wouldn't have changed the behavior any. The coolant would have started flowing at a lower temp, but the same steady state temp would have been reached. Thermostat's don't add cooling capacity.
Back to oil temp. Finally what I did was duct a lot of air flow at the race car's AL oil pan. That reduced oil temps a surprising amount. I tested that idea a lot and ultimately left the oil cooler off. Unexpectedly, as long as I ensure there was lots of air blast on the oil pan, I dumped as much thermal energy from my oil as my oil cooler did. And since "simple"= "reliable", leaving the oil cooler off was a net gain.
How this affects transmission temps. Well, mostly it doesn't. I think that the transmission fluid also goes thru a heat exchanger so that warm coolant can speed the warming of the tranny fluid. But we have no tranny fluid cooler. As long as your tranny fluid is in good shape, it should stay a fair amount cooler then your coolant. If you're getting tranny temps >200deg, I'd immed change your fluid. The idea that tranny fluid is a "lifetime fill" is one of the lies of our age.