A cooling system in which an electronic or other component is cooled by using one or more solid sources of liquid vapor in conjunction with one or more high-temperature vapor sorbents or desiccants that effectively transfer heat from the component to the fluid in the wellbore. The latent heats associated with phase changes and dehydration of a hydrate can provide substantial cooling capacity per unit volume of hydrate, which is particularly important in those applications where space is limited. According to the present invention, a sorption cooling and heating system is provided for use in a well, such as downhole tool which is in a drill string through which a drilling fluid flows, or in a downhole tool, which is on a wireline. Electronics, sensors, or clocks adjacent to a hydrate are not only kept cool by the heat sinking effect of hydrate phase changes and evaporation of water that is released but, during phase changes, they are being kept at a constant temperature for extended periods of time, which further improves their stability. Furthermore, such a system can also be used to heat a sample chamber or other component by placing it adjacent to the high-temperature sorbent or desiccant that heats up as it adsorbs the water vapor that was released by a low-temperature hydrate or desiccant during dehydration.