Thank you all for your advice,
MJCronin, a hot water tank is a fine idea, but for our application it would have to be quite a large tank, and we simply don't have the space to accommodate it. Thank you for the suggestion, though.
Otherwise, it looks like we'll be pursuing a system similar to what LittleInch has suggested. We will measure the water outlet temperature and adjust the hot oil inlet with a control valve. When hot water use is no longer needed, we will close the hot oil inlet and run cold water through the exchanger to cool off the hot oil to a safe temperature. Oil will be on the tube side, and a relatively low amount of water will be necessary to cool the oil.
For safety, thermocouples will gauge the temperature of the water inside the heat exchanger; if the water gets too hot and is approaching boiling (in the event of a failure of the previous control system), then another control valve will open to run cold water through the system, and set off an alarm. For a total failsafe, a pressure relief valve will be vented to a safe location.
I'll be consulting with one of our senior engineers about the project, but I just thought I would get a wider range of opinions from y'all. Thank you!