EMB-145 Captain reported the flight was dispatched with one pack inop. During climbout the other pack failed. The crew received priority handling and return to the origin airport.

Narrative

Passing around 15;000 ft. on our way to initial level off at 16000 ft.; we had a pack 1 valve closed EICAS message followed quickly by Pack 1 OVHT.Note: Pack 2 was deferred as it had failed during the very first flight we had early in the morning.We advised ATC of the need to level off at 16;000 so rejected the further climb instruction due to a potential issue. We were at that altitude for approximately 1-2 minutes.We ran the QRH; the message disappeared; but quickly reappeared. We attempted it twice more but the message disappeared and reappeared every time. We made the decision to divert back to ZZZ at that point as it wouldn't have been possible to fly to the destination at such a low altitude.We then requested 10;000 ft. and then even lower.During this time; I communicated with dispatch and as expected; they advised us return to the field.I calculated the fuel we needed to burn and needed 45 minutes of hold time with gear and flaps 9 extended to prevent an overweight landing.Maintenance via dispatch advised that it would be acceptable to land overweight as long as our ROD didn't exceed 360 ft/min.We kept that in mind just in case any one of our passengers or crews health/situation would deteriorate in the higher than normal temperatures. We also stayed close to the airport for this reason.We didn't deem it necessary to [request priority] as I believe the situation didn't warrant one.I called our Flight Attendant (FA) using the Cabin Emer call button; providing her with a report and made 4 total passenger announcements of which 3 were in cruise. The FA advised me that she handed out water during the entire ordeal.The cockpit rose to 39 Celsius for around 30 minutes and the cabin was 28 Celsius during the situation. My company-issued EFB also overheated.Further note: upon landing; we opened the Direct Vision windows due to the high sustained heat. Maintenance personnel saw this as well as they approached the aircraft on arrival in the gate. I called Maintenance later to tell them verbally to which he responded that he'll get someone to record it.