I apply the heat lamp and cool down after my stretching sessions. I do not know what drives my gains (stretching intensity, heat lamp and/or cooling down). But it works for me in that combination and I am not going to change anything to the setting as long as I see gains. So I guess that’s a “thumbs-up” for cooling down, at least for me.
I guess it is just up to you, to try it out for yourself. By the way, I cool down in the shower with freezing cold water for a couple of minutes.