Captain reported an immediate descent and air turn back after loss of both packs during climb.

Narrative

Ferry flight; ZZZ2-ZZZ3. Aircraft X. Roughly 8 minutes after takeoff; BLEED TRIP OFF light illuminated. Run the QRH and finally directed us to turn off the affected side PACK; which was the left pack. Few seconds after turning off the left PACK; the right PACK light comes on. We were cleared by ATC for FL280; at that moment stopped at FL200 and Request descend and back to ZZZ1.We were cleared direct to ZZZ1 and decent to 10;000 ft. by ATC. We read the check list for right PACK light ;while we were on the check list; Cabin Altitude warning horn activated during descend; CABIN ALT exceeded above 15;000 ft. and passenger oxygen masks deployed. We read the check list for (Cabin altitude or rapid decompression) we use oxygen mask until 10;000 feet. Didn't [request priority handling] because situation was on the control.We didn't see any PACK overheat indication on the ground and before takeoff. Approximately 8 minutes after takeoff we noticed with the first indication which was left BLEED TRIP light followed by right PACK light. Had 45 minutes ground stop in ZZZ2. PACK was running for cooling purposes and cause PACK overheat in flight.We decided to stop climbing at FL200; and run the check list for left BLEED TRIP light. Eventually QRH directed us to shut down the left PACK; immediately after that the right PACK light comes on; at that point we decided to request descend to lower altitude and back to ZZZ1. We definitely need some equipment on the ground to keep the airplane cool during summer especially in hot airports.