How do visitor flows at open-air archaeological sites respond to extreme weather, and to heat in particular? Open-air sites such as Castelseprio and the Valcamonica rock-art parks are physically exposed in a way that indoor museums are not, so as summers warm they face a demand risk that indoor institutions do not share. Using a daily attendance panel for Castelseprio (December 2023-June 2026, 762 days) merged with local weather data, attendance follows an inverted-U shape in temperature, peaking at 20-24C and falling sharply above 35C (about -51%) and in rain (about -33%), with the sign on rain reversed relative to published evidence on indoor museums. The core result is established on one site; a proposed multi-site panel across thirteen Lombardy museums (indoor and open-air) would identify the mechanism and support a roughly fivefold gain in precision.