Luckily, this is a very simple food safety issue that is very easy to explain and implement, and is considered a requirement for professional food service establishments.
The basics of this procedure is that foods that have been properly cooked and then properly cooled can be served at any temperature, provided it is being served immediately. An example of this is the beef in a roast beef sandwich. At home, a lot of people (I will admit I do this myself), will grab something from the fridge and eat it cold or throw it into the microwave for a couple of seconds to add a little bit of heat to it, which is perfectly acceptable, again, provided it is served and eaten immediately.
The situation with properly reheating foods occurs when you are reheating foods for hot holding on a buffet or for later table service. At that point, all reheated items must be moved through the temperature danger zone as quickly as possible. The food service requirement is that the food must be heated to an internal temperature of 165 degrees F (74C) and hold that temperature for at least 15 seconds. This reheating must be completed within two (2) hours.
If you have any questions about anything that I present in these lessons, or have a question about anything regarding food safety, please feel free to contact me.
Tomorrows lesson: Proper cooking temperature endpoints for food safety.