The use of lightweight materials in the automotive industry for structural parts has been increasing in recent years in order to reduce the overall vehicle's weight. New innovative lighter materials are being developed nowadays to accomplish that objective. In order to keep or even increase passenger's safety, structural parts made of these materials need to withstand static and impact loads within a range of different temperatures along the vehicle's life. The effect of these conditions when joining these dissimilar lighter materials is a critical issue to be considered when designing the car's body. In this paper, the strength under real car conditions of single lap joints (SLP) made of aluminum alloy (AA) bonded to carbon fiber reinforced polymer (CFRP) adherends was studied. A new crash-resistant epoxy adhesive was used to bond these lightweight materials and an extended characterization of its cohesive properties was carried out. The single lap joints were tested at temperatures of −30, +23, and +80 °C under quasi-static and impact loading. The data obtained was used to perform simple numerical models of the single lap joints under static and impact loads. The experimental results showed an expected increase of the joints strength with the strain rate. The joints behavior was highly influenced by the adherends, especially by the aluminum yielding at high and room temperatures. Delamination of the composite was obtained at low and room temperatures, which explained the strain rate dependence of the failure load. The numerical models predicted with good accuracy the strength of the joints under both static and impact loads.