An example of a situation where no heat is added to or removed from a system, but the temperature of the system changes, is the process of adiabatic compression or expansion of a gas.

Adiabatic Compression: Consider a cylinder with a piston containing a gas. If you rapidly push the piston down, compressing the gas, and do so quickly enough that there is not enough time for heat exchange with the surroundings, the process is considered adiabatic. In this case, no heat is added to or removed from the system. However, the compression work done on the gas increases its internal energy, which results in an increase in temperature.

Adiabatic Expansion: Similarly, if you rapidly pull the piston up, allowing the gas to expand, and do so quickly enough that there is no heat exchange with the surroundings, the process is adiabatic. The gas does work on the piston, which decreases its internal energy and results in a decrease in temperature.

In both cases, the temperature of the gas changes due to the compression or expansion work done on or by the gas, even though no heat is transferred to or from the surroundings. This demonstrates that a change in temperature can occur without any heat exchange, as long as work is done on or by the system.

It's important to note that the adiabatic process is an idealization and may not perfectly occur in real-world situations, as there might always be some level of heat exchange, even if it's very small. However, the concept illustrates the principle that a change in temperature can be achieved without adding or removing heat from a system.