I don't necessarily run a higher weight in the summer, but I do prefer the keep the viscosity spread less in summertime. For example instead of 5w-30, I might run 10w-30.
There's just no need for a 5w, 0w, etc. in my climate in the summer. Since additives / viscosity improvers can break down in the presence of heat, the oil should be more robust without them, or less of them. In no way am I suggesting this is a blanket statement for all oils, it is NOT. Some oils may not have additional components to yield a high viscosity spread, I get that. It's just erring on the side of caution and the plain fact that anything less than 10w is completely unnecessary for most of the year where I live.
And to the OP: The engine oil temperature is greater in summer, without a doubt. Drive your car for an hour in stop and go traffic in July versus January and measure the oil temperature. You will get two very different results! Sure, "operating temperature" or coolant temperature may be the same or similar, but oil temperature will not.