Organisms like plants, humans or bacteria are self-sustaining systems of chemical reactions. Temperature can affect the rate of chemical reactions, so temperature can affect the rate of metabolism in plants and other organisms.
For any chemical reaction to take place, reactant molecules must collide in the right spatial orientation and with sufficient energy for a reaction to take place. Temperature is the average kinetic energy or energy of motion of molecules in a substance, so the higher the temperature, the more collisions with sufficient energy will take place and the rate of the reaction will increase.
Cellular respiration is a series of reactions that breaks down sugars to extract energy. Since chemical reactions proceed more rapidly when the temperature increases, the rate of cellular respiration increases with temperature and approximately doubles with each increase of 10 degrees Celsius (18 degrees Fahrenheit).
Temperature also affects the activity of enzymes, large proteins that catalyse or speed up reactions. Most of the key reactions in cellular respiration are enzyme-catalysed. Enzymes are most effective at an optimal temperature -- increasing the temperature too much, for example, can denature the enzyme or cause it to lose its shape. Consequently, temperature increases the rate of cellular respiration but cannot do so indefinitely.