Plants, like all living things, need water to grow, but the temperature of the water can have an effect on that growth. There is not complete consensus on the effect of warm water on plant growth, but there have been studies showing definite differences, albeit somewhat slight.
In an experiment conducted in Louisiana under the direction of John I. Swang, Ph.D., students used three different temperatures of water to determine what effect this had on the plant growth. The "hot" water was at a temperature of 55 degrees Celsius, the "warm" water was at 43 degrees Celsius, and the "cold" water was at 36 degrees Celsius. The hot water produced the tallest plants with the fewest leaves, while the cold water had the shortest plants with the most leaves.
It should be noted that in the Louisiana experiment, the hot water was not close to boiling, nor was the cold water close to freezing. A sharp extreme in temperature is not conducive to healthy plant growth, and in fact, it can even kill the plant.
Though the most common usage for warm water with plant care is the watering of the roots through the soil, it can also be used in other ways to tend the plant. Aggie Horticulture, an information provider for Texas A&M University System Horticulture program, recommends using warm water with a little mild soap to keep leaves of house plants dust-free, making sure that the soap does not drip on the soil.
Not to forget aquatic plants, there are obviously many plants that live completely underwater and do very well in that habitat. However, when the water is warmer, the plants often grow better and have a longer growing season.
One of the upsides to cold water for some plants is that it can actually hold more oxygen. For this reason, some plants that are high in oxygen needs do better in these cooler temperatures.