B737 Captain reported a lack of coordination and communications problems overly complicated a maintenance situation and resulted in a late departure after an aircraft swap.

Narrative

Upon arrival to the gate; I walked down the jet way to find my Flight Attendant were off the aircraft due to excess heat from the ground air. As I recognized that; local maintenance also stopped me on the jet way and briefed me on a lack of pass down between days and mids letting me know that the aircraft needed a part and would be delayed a few hours. As I was just at the CS (customer service) desk; they had expected to board in a just a few minutes after I had arrived. There was not much coordination between MM and other operational team members. Additionally; we told the MM that we were unable to even wait on the aircraft for the part since it was too hot. MM had the ground air disconnected and started the APU and packs.After review of the paperwork; it was found that there was a lingering wing body overheat issue. It was cleared and signed off; then repeated a second time. MM was going to replace the box that monitors this function and the part was to be delivered from an aircraft arriving from ZZZ. The part was to arrive at XA:00 and an XA:35 time was scheduled for the late departure. This time was not borne in reality; as there is both box verification; testing; engine run; and actual verification that the box was the problem rather than duct work; which is the real purpose of the light for wing body overheat. Upon seeing all of this; I decided to further investigate.The flight deck and aircraft had by then cooled off sufficiently to board the aircraft and look at some indications; as well as communicate to local entities by the radio. On the flight deck; there were an unusual amount of indicator lights on; not typical of an APU running with packs on. After review; it was discovered that the battery had a very high discharge rate; likely caused by the second discovery; that MM had not connected either ground power or the APU to the aircraft power system. Additionally; they were running the packs with the wing body overheat light illuminated; and it was unclear whether they had eliminated the duct leak as an issue prior to operating flow into the duct. While I realize MM still owns the aircraft; I did not see that as a safe practice and advised them; especially as our Quick Reference Handbook addresses the idea that the APU Bleed would be turned off as part of the procedure to isolate the wing body. MM was informed and there was a good debrief completed concerning the wing body overheat pack operation off the APU. Nonetheless; they understood the idea that operation in this manner; beyond the Quick Reference Handbook; may not be a best practice.So; as the safety item is resolved; we were left with two other glaring issues. First; initial coordination between MM and operations/CS was not good; and thus no one really knew what was going on. I can see both sides having issues here; as gate CS eventually came down to close the door to our replacement aircraft and finally recognized; after both chat and the Captain making an appearance; that the entire jet way was filled with people who needed to gate check bags. MM was responsible for the initial issues and pass down was poor. Second; flow up to ops manager/router was also poor; as no one really saw the issue for what is was: not an XA:35 departure delayed for a part; but an issue requiring a day to solve that no one really wanted to admit was a problem (look at the history). The Captain had to speak with higher authority and get the Ops Center involved so that the delay did not get even further out of hand. The delay was limited because this interaction took place; and if not could have been much longer; for really no good reason. We need to address items like these so we can do so.