B737 First Officer reported a APU failure on the ground which resulted in an aircraft refusal.

Narrative

We were given a last minute swap to the incident aircraft after a previous crew refused the aircraft - unknown to us until the gate agents told us about it and I found notes in the flight feed saying so; as they did not follow procedure and make an ELB (electronic Logbook) entry. Upon arrival to the aircraft to operate our flight to ZZZ1; it was discovered that the ground air hadn't been connected and the plane had been sitting for several hours. It was over 105F onboard the aircraft (about 96 degrees outside in ZZZ2 at the time) and the APU was placarded and collared inop due to an inop fire detection loop deferral that was applied. Talking to ramp; they told us the Power Control Unit (PCU) ground air at that gate; X didn't really function well and was blowing hot; so that's why it had been disconnected. The Captain and I discussed the issue and agreed there was no way we could safely or acceptably board passengers onto the airplane without any way to keep them cool. He refused the airplane and dispatch said they would notify Maintenance. I said that per our bulletin we needed to send the Maintenance Request Manual (MRM) refusal code to get it into the logbook; however after 3 attempts I kept getting an error message when attempting to put it into the ELB. The Captain (CA) called and spoke to Maintenance directly to enter it and I verified it did get put into the logbook. However; I don't believe Maintenance properly documented it as an aircraft refusal; because it seemed to take about 45 min for the station to understand what was going on and they were still trying to load bags onto the aircraft until we stopped them and zone was calling the gate agents saying 'Oh it's good to board now'; while we were there saying 'No; it isn't' Finally; the station appeared to get the memo and the flight was delayed 10 hours and we went to the ZZZ2 Hotel. Upon arrival 10 hrs. later to operate the previous day's flight.... we had the same airplane. It had been sitting there all 10 hours; with no apparent attempt to fix anything and still assigned to us; the crew who had refused it. This time the ground air was hooked up although still not blowing much for cold air. However; it had just started to heat up for the day and the airplane was much cooler than the prior day due to the ambient temp in ZZZ2 only being about 75F at this point; so to get the delayed passengers on the way we did take the jet at this point. There were a few failures here that it would be great if the company could address. Aircraft with inoperative APUs shouldn't be dispatched to stations over 90 degrees; but if they are; need to be put on a gate with functional cooling PCU that stays on so the aircraft can't get heat-soaked beyond the capabilities of PC ground air. Aircraft refusal process is still a bit of a mess; and a crew that refuses an aircraft should be swapped; not delayed 10 hours right back into the same aircraft. They should not have been shopping the jet to us in the first place after the first crew refused it.