Visual contrast, not radiant heat — the actual mechanism
It's a reasonable guess that insects climbing toward the sun are chasing light. They aren't — and the fuller story isn't simply heat either, though heat plays a real supporting role. Field research on the multicolored Asian lady beetle — the species most homeowners are actually seeing in these clusters — tracked the actual fall flight in open-field conditions and found the landing cue is high visual contrast: dark-on-light linear silhouettes such as painted trim, gutters, drainpipes, window frames and the hard-edged shadows a house casts (Nalepa, Kennedy & Brownie, 2005, Environmental Entomology). The study is explicit that beetles are "not visually attracted to the color white per se," and it calls into question an earlier, widely repeated belief that they're simply drawn to bright, reflective surfaces.
Warmth still matters, but it answers a different question: not where they land, but when they fly. University of Illinois Extension documents that overwintering insects concentrate on the walls and wall voids that run warmest — in New Hampshire that's almost always the south wall and the sun-exposed portions of the east and west walls, since the low fall sun angle keeps those surfaces warm well into the afternoon even as air temperature drops. A warm afternoon after a cold night is what gets a fall flight moving; once beetles are airborne, it's the high-contrast silhouette on that same sunlit wall — not the heat itself — that pulls them in to land. The two facts point at the same walls for different reasons, which is why the sunny-side pattern is so consistent. Boxelder bugs, brown marmorated stink bugs and cluster flies mass on the same sun-exposed walls on warm fall afternoons, but the visual-contrast landing cue has only been established for lady beetles — the mechanism for the other three hasn't been isolated the same way.

