I’m using the similar, but cheaper Harbor Freight “Apache” cases to house stationary relays. Same snug fitted foam. I’ve painted the cases reflective white. It’s been cool here since they’ve gone online, so no real testing of potential heat=related issues.
My theory is to keep the foam packed in, as it reduces the transmission of heat into the interior. If it was open air inside it would heat more quickly. The question is whether night time cooling will be enough to offset daytime solar heating up on the roof now that warmer weather is on its way.
One additional note. I’m using the medium size “Apache” case. It is considerably larger than the Pelican case pictured above, looks like this.
More foam fits on top of this arrangement, cut to fit closely around it, filling the case; it’s removed here to show the GTM and battery pack. So is there much more insulation around the components inside. While they do make some heat that could be trapped, I suspect heat generated in the interior is far less than that from the input of exterior solar heating.