How can I measure when a solid releases the greatest amount of heat per mole?
You can use calorimetry. This is a process in which a substance is added to water which is in a well insulated container. A thermometer is placed in the water and when the substance is added the temperature change is recorded over a period of time. By graphing the change in temperature (on the y-axis) vs. time (on the x-axis) you can see if the temperature is linear over time ( meaning the change in temperature is about equal for each time interval you measure) or non-linear. If it is non-linear you may see a large change initially and then a leveling out of the temperature over time.