A building cover element is described with at least one, preferably stationary arranged fastening device, which comprises an exterior section aligned to the exterior of a building to be provided with the building cover element, comprising at least one film element, which shows an exterior film layer to be arranged at the exterior of the building and anchored with an edge section at the fastening device, and with at least one thermally insulating element. The thermally insulating element is arranged with a first section at the exterior section of the fastening device and with at least one second section resting on the edge section of the exterior film layer of at least one film element.