I don't think so
I've had many experiences with strictly oil cooled engines. In particular the 1986 Suzuki GSXR 750/1100 platform.
They went strictly oil cooled with a giant oil cooler and 8 quarts of oil.
As you can see, this motor is filled with oil galleys and has no coolant or radiator.
Another note, I live in the desert of the US Southwest where temperatures exceed 120F in the shade during late June to August.
I have never had an issue running 10w-40, 20w-40, 20w-50....so on. Although the 10w-40 is 'less dense' than 20w-50, in theory, I have not detected a difference in power, cooling or engine life.
Certainly, comparing this engine to your liquid cooled modern car platform might seem ludicrous but at the end of the day taking the motor I am talking about to a track and running it a very high RPM's in desert summer heat and not detecting a difference in cooling is pretty meaningful.
I check radiator water constantly and refill it if needed.
If you are needing to refill your coolant on a semi-regular basis I suggest you focus on your actual cooling system.
I haven't added coolant to my 2013 Toyota Truck for at least 6 months and I'm sure I'll be able to get to summer before I add a little to the reserve reservoir.
IMO, focus on the actual cooling system.