A CRJ-200 Captain reported losing cabin pressure when the sole operating pack failed due to high temperature. He declared an emergency and descended to a safe altitude where the pack was successfully reset and the flight continued.

Narrative

As we were climbing out we were told to cross [an] intersection at or above FL240 on our way to FL250 due to military activity. We reached FL240 on the airway and then we received a R PACK HI TEMP caution message. This was an issue because the left pack was on MEL. I informed ATC of what had just happened and said that we needed lower. The First Officer was flying and started to initiate a descent down to a safe altitude. At first ATC only cleared us to FL210 due to traffic; I do not think they realized what was happening when I told them we had lost both packs on the aircraft. I then declared an emergency with ATC and told them that we were proceeding to FL100 and that we would take any heading needed to avoid the traffic underneath us. The traffic was at FL190 and as we passed thru FL210 we received a TCAS TA and the Controller assigned us a heading of 270 to take us away from the other aircraft. The First Officer was flying and not only did an excellent job of maintaining aircraft control during the rapid descent; but he also acquired and maintained visual contact with the other aircraft outside of the right window. Upon reaching FL100 we ran the QRH and managed to get the right pack working and the right 10th stage bleed valve to open. We told ATC that we regained the pack and that we were no longer in an emergency situation. We then asked for clearance back to FL200; as I did not want to take the aircraft to the maximum single pack altitude and possibly over stress the pack and cause another failure. The pack functioned normally for the rest of the flight. After climbing back up toward FL200 I asked ATC if any paperwork needed to be sent in or if I should call or contact the facility in regards to declaring the emergency; as we had to rapidly descend to FL100 while nearby another aircraft. Also; we may or may not have entered the military area we were initially cleared over before the event occurred. The Controller replied that no phone calls or paperwork would be necessary in regards to what had happened. After landing I contacted Maintenance and they came out to inspect the pack. They did not note any faults or abnormalities; and the pack functioned normally for the next two flights that we had. They also cleared the other pack MEL so we had both working for the rest of the day.