We present spatial variations of the CO J = 2-1/1-0 line ratio in the barred spiral galaxy M83 using Total Power Array (single-dish telescopes) data from the Atacama Large Millimeter/submillimeter Array. While the intensities of these two lines correlate tightly, varies over the disk, with a disk average ratio of 0.69, and shows the galactic center and a two-arm spiral pattern. It is high (0.7) in regions of high molecular gas surface density (Σmol), but ranges from low to high ratios in regions of low Σmol. The ratio correlates well with the spatial distributions and intensities of far-ultraviolet (FUV) and infrared (IR) emissions, with FUV being the best correlated. It also correlates better with the ratio of specific intensities at 70 and 350 μm, a proxy for dust temperature, than with the IR intensities. Taken together, these results suggest either a direct or indirect link between the dust heating by the interstellar radiation field and the condition of giant molecular clouds (GMCs), even though no efficient mechanism is known for a thermal coupling of dust and bulk gas in GMCs. We speculate that the large spread of in low Σmol regions, mostly at the downstream sides of spiral arms, may be due to the evolution of massive stars after spiral arm passage. Having in a late phase escaped from the spiral arms and their parental clouds, they may contribute to the dust heating by FUV and gas heating by cosmic rays produced by supernovae.