Compared with traditional static insulation, a thermally switchable building envelope could reduce annual heating and cooling loads by intermittently coupling to the outside environment when beneficial. Here, we demonstrate a voltage-actuated, contact/non-contact thermal switch that meets the unique challenges of this application. The switch is non-volatile, consuming electricity only briefly while switching and none to hold steady state. The switch ratio is 12, the off state has a low effective thermal conductivity of 0.045Wm-1K-1, comparable to fiberglass insulation, and the performance is stable over 1,000 switching cycles. Numerical simulations using real-world climate data show that combining this thermal switch with a thermal storage layer in a building envelope can yield annual energy savings of 9%–55% (heating) and 17%–76% (air conditioning), depending on the climate zone. The greatest benefits are realized when the exterior temperature crosses well above and below the desired interior temperature within a single 24 h period.