Thanks for the replies, everyone.
I don't think I am expecting miracles out of the solar cover. In fact, the main reasons for using it have always been less evaporation, retention of heat gained during the day, and a lowering of my liquid chlorine requirements when in use.
However, that said, I have to argue in favor of the solar cover actually having a genuine effect on temperature gain. My company makes equipment that is normally used to track concrete temperatures (every 10 minutes) and I have two years of temperature records for the deep end of my pool, one year without a solar cover and one year with the new solar cover. There is absolutely no question that the solar cover makes the water temperature rise faster in the spring over time than not having one. Over the course of 30 days, for example, between Apr 15 and May 15, the uncovered pool gained 0.5 degrees per day on average, and with the cover gained 1.1 degree per day. Ambient temperatures and solar availability were about the same for each time period. I ran the pump at various times during each time period also, and it should be noted that running the pump had a significant effect on water temperature gain rate. Until I installed my pump timer, I would have to manually turn it on and off. The stunning rise in temperature when the pump had been running for an hour or so after not having been run was amazing. Thermal stratification exists in both scenarios, but is vastly higher with the cover on. When that 6-8" of hot water on top gets circulated through the pool, it most definitely has an effect.
My pool water is currently a brisk 42F in the deep end right now, with my safety cover still on and the pool still closed, so no circulation.