B737 Captain reported a flight was boarded without pilots and cabin temperature became excessive without conditioned air; resulting in passenger illness. The Captain attempted to deplane the aircraft for passenger safety but company operations refused the Captains request.

Narrative

I was reassigned to operate XXXX ZZZ-ZZZ1. This was a last minute assignment and boarding was complete before the First Officer (FO) and I arrived. ZZZ Operations boarded the flight without a working PA system; external air or APU air and it got so hot that a passenger had to be removed because they were having a seizure or a stroke (or both). The non working items and heat levels were all noted in the communications; and responded to by ZZZ Operations before boarding began. The passenger was transported to the hospital and did not fly with us yesterday. I was preparing for the flight in the terminal; and following along in chat; and after the medical event with it still hot on board I told ZZZ Operations to deplane the aircraft. When I arrived at the gate; the agent told me that they offered egress and no one wanted to get off. When I went down to the aircraft; I learned that the agents had stopped the Flight Attendants from making an announcement to offer egress. At this point; they had all been on the aircraft for almost an hour; with all but 5 minutes of that time without any type of air circulation; or PA system because the battery was off. Maintenance was walking off the aircraft having started the APU as I arrived. Obviously the heat created a safety issue; and not having a PA available made it very difficult for the Flight Attendant crew to handle the medical problem while boarding was finishing up. As I was starting my aircraft preflight; the agent walked up to me with a phone number for operations; which I called. The operations manager" said that they needed the gate for Aircraft Y from ZZZZ and basically told me to do whatever I could to hurry up. He actually said; I hope you can do what you can at a safe speed to make the gate available; or something like that; but the undertone of the conversation was clear. Separately; I told the agent to deplane the aircraft after the medical problem was removed from the aircraft; and while the flight attendant crew attempted to follow my direction; the gate agent actively defied it; and then lied to my face when I arrived telling me that no one wanted to get off the aircraft. My FO witnessed this; and his recollection was the same. So; with this situation there are a few issues with SOP compliance; safety policy questions; and Captain authority questions.I don't want to live through another XXX; and that's really the way that this situation was headed yesterday. No one on the Airport Customer Service side; or ZZZ Operations seems to care; unfortunately. Seems that there are 3 issues- 1. Operational process to begin and continue boarding under adverse circumstances. 2. Handling of a Medical Event seemingly due to extreme heat and the protection of others exposed. 3. Subversion of Captain's Authority by failing to follow direction to deplane the aircraft due to a safety issue."