It would depend upon how you define "hot". What is hot to you is not necessarily hot to an engine, or the lube.
Many SAE studies that involve oil for diesel applications are run with the sump temps at 250F; this is to induce a scenario that would mimic heavy loading (say 80% throttle) in terms of a HALT (highly accelerated life test). That temp is well within the definition of "normal" for a sump temp.
Now - I suppose you're going to say "Yabut Dave .... turbos get really really hot; with EGTs up to 1600F ...."
Well, that is true. But the OIL does not get that hot. This is a topic of thermal energy transfer, in which temps are only one portion of the equation. Oil can do many things, and transferring thermal energy is one of them. They absorb/reject heat depending upon a temp delta and many other things. As long as the lube system is designed for the right volumetric flow rates and capacity, including absorption and rejection heat exchangers, then all will be fine.
Time for me to dust off an old example ...
Go into the kitchen and light a small candle, and prepare to hold a paper napkin above it. The purpose of the exercise is to keep the flame from lighting the paper on fire.
- Now, pass your fingers quickly over the flame just an inch above the flame. No damage done to your fingers, because very little energy was absorbed by your fingers. Most of the energy goes right into the napkin and it burns.
- Next, pass your fingers at a moderate speed over the flame. You fingers will be warm, but not hurt. You pulled heat from the source and your skin/blood transferred that energy to a larger mass (your body). And some goes into the air towards the napkin. If you, and some friends, could pass fingers over the flame, you'd be able to protect the napkin from damage and yet not sustain finger burns.
- Now, hold your fingers steady at the flame and don't move them, if you dare. You'll get a 3rd degree burn, and either temporary or permanent flesh damage will result. While the napkin is fine, your fingers are not.
There would be a point of balance where you could carry away enough heat energy with enough fingers that no finger would ever be damaged, and no overheating of the napkin would take place. The challenge is to engineer the rate of thermal exchange so that the desired outcome happens without damage to the primary medium. If you had enough fingers, and the right velocity of passing your fingers over the flame, you can find a point where no damage happens to the fingers or the napkin.
Get the point?
Thermal energy exchange is a matter of using one mass to transfer energy to another mass. As long as the lube system is properly sized and designed, there should be an adequate flow of lube to carry the heat away to another place, and as long as those volumetric flow rates and exchange conditions are favorable, no harm is done. A lube system can easily sustain very high local temps as long as the exchange rate and rejection point are properly engineered. Whereas a turbo may see EGTS as high as 1600F, the oil won't get that hot. It will flow enough volume and velocity to only pick up a portion of that energy, in an ever-revolving exchange as each quart passes over the "hot spot". The oil then rejects the heat into another place (typically an air or liquid cooled exhanger). Further, as a generalization, both conventional lubes and synthetic lubes both absorb/reject energy at the same rate; it's not like syn lubes can transfer "heat" substantially quicker. Whereas there may exist a tiny, fractional benefit one way or another, it's absurdly small if it exists at all (well within any practical means of the error in measurement).
If you want to have a discussion about "hot" oil, then you'll need to define the temps, the sump size, the heat exchanger size, the secondary medium (air or coolant), the flow rate at the hot-spot, etc. Until you can do that, it's just silly banter. Suffice it to say that "hot" to you does not really equate to "hot" to the oil. A well designed system will avoid overheating the lube.
And I would note this as well ... any lube that gets damaged from thermal over-exposure is not a fault of the lube, but a flaw in the design of the lube system. It's not the oil's fault that the rate of thermal exchange was exceeded. If you have a system that absolutely requires syn lubes, so that the oil is not damaged in use, then I'd argue that you have a system that is not designed well. At some point, ANY lube can get to a thermal point that it gets compromised. It may just take longer to happen to a syn lube.