The performance of superconducting radio-frequency (SRF) cavities depends on the niobium surface condition. Recently, various heat-treatment methods have been investigated to achieve unprecedented high quality factor (Q) and high accelerating field (E). We report the influence of a new baking process called furnace baking on the Q-E behavior of 1.3 GHz SRF cavities. Furnace baking is performed as the final step of the cavity surface treatment; the cavities are heated in a vacuum furnace for 3 h, followed by high-pressure rinsing and radio-frequency measurement. This method is simpler and potentially more reliable than previously reported heat-treatment methods, and it is therefore, easier to apply to the SRF cavities. We find that the quality factor is increased after furnace baking at temperatures ranging from 300C to 400C, while strong decreasing the quality factor at high accelerating field is observed after furnace baking at temperatures ranging from 600C to 800C. We find significant differences in the surface resistance for various processing temperatures.