If I understand correctly, the alligator can choose to either pump blood to quickly equalize with the surrounding temperature, or not pump blood to get more isolation.
In the morning when it wanted to heat up after the night it pumped blood. In the afternoon when it was already warm enough and the ambient temperature was too warm, it stopped pumping blood.
Thanks, your way of stating it makes more sense to me. This sort of faculty would be used whenever the ambient temperature is closer to "optimal activity temperature" than the body is. Like you say, typically mid-morning when the environment has warmed up but the body hasn't. I suppose it could also work in the evening after a really hot day when it would be good to cool the body...