Yes! If you take an ice cube rack filled with hot water and put it in an iced-up freezer, the ice cubes will form noticably faster than if you use cold water. This phenomenon was first observed by Aristotle:

"Many people, when they want to cool water quickly begin by putting it in the sun. So the inhabitants when they encamp on the ice to fish (they cut a hole in the ice and then fish) pour warm water round their rods that it may freeze the quicker; for they use ice like lead to fix the rods."

Sir Francis Bacon noticed the same phenomenon when wooden pails were placed on ice. Those with hot water froze faster. There are two major types of explanations for this phenomenon. Either or both may be true, depending on the conditions of the experiment.

Explanation 1: Thermal Contact If you put an ice-cube tray with hot water into a freezer with ice covering the shelf surface, the hot water will melt a little bit of the ice on the shelf. This then refreezes, making better thermal contact between the freezer and the tray. As a result, heat is conducted away more quickly from the water, allowing it to freeze faster.

Explanation 2: Convection It has been noticed that even a metal pail of water suspended in the air on a chilly night will freeze faster if the water is warm. Thermal contact is not the issue here. Instead, it is hypothesized that convection may be the contributing factor. In a pail of cold water, the water is stationary, and freezing begins on the edges of the pail and surface of the water and slowly works its way inside. The core, now insulated by a chamber of ice, freezes more slowly . However, a warm pail of water, when cooled at the edges, will start to churn due to convection. This mixes the water, allowing it to cool more evenly, potentially speeding up the freezing process. The degree of temperature difference determines the amount of convection that occurs.

Obviously, the conditions of the experiment are crucial here. The relative temperature of the water and the environment, the type of container, its size and shape, thermal contact with ice, etc. These all affect the rate of cooling and freezing.