The tensile, compressive and shear behavior of standardized specimens cut from a veneered balsa wood used as structural sandwich core was investigated at ambient temperatures of up to 250 °C. The average moisture content was 9.1%. The specimens’ responses were strongly affected by the configuration of the veneer layers. Specimens with a higher number of 0° veneer layers in the loading direction exhibited higher strength and stiffness at each temperature. Independent of the loading type, the specimens gradually lost strength and stiffness up to the wood-burning temperature of 250 °C due to the softening of the hemicellulose and lignin. Smaller cross sections with more surfaces cut perpendicular to the grain dried faster and thus delayed the degradation of properties. The dominant failure modes did not change with increasing temperature if the behavior remained either fiber- or matrix-dominated. The failure mode changed if the behavior shifted from fiber-dominated at lower temperatures to matrix-dominated at higher temperatures. The degradation of the properties of the adhesive between the veneer layers affected specimen behavior only at the highest temperature.