My guess is the cap may be a coincidence unless it's trapping the heat. Most don't as they don't fit well enough to do so to be honest. Just a function of standard size caps and varying size tubs.
What you are seeing happens with spa covers. On the hot days, the PVC vinyl is expanding allowing more space in between the vinyl jacket and the foam cores. Air produced by running your blower or in some cases just normal off-gassing naturally rises. There's just more room inside the jacket now for it to go. The reason it recedes on the cold days is that the vinyl is shrinking back.
Depending on the color of your cover, the use of the silver cap may help the situation by reflecting some sun away. Of course, if the cap is super tight that could also cause you some issues. The main thing you want to avoid is the foam melting inside the cover. It's rare, but we've seen it. Anyone that has their spa installed in a lot of direct sunlight should avoid the dark vinyl colors. Most of the melted foam we've seen over the years come from when spas are parked right up against a southern facing brick facade of a home and when there is a window located in a place that can reflect sunlight down onto the spa's cover.
I know it's not super-definitive and there's a lot to consider there, but I hope it helps.
