B737 pilots reported they were unable to control the passenger cabin temperature and returned to the gate.

Narrative

Pilots arrived at aircraft approx 10 mins prior to dept due to late inbound from ZZZZ and needing to clear customs. Flight was already fully boarded when we arrived. Upon first arriving. Flight Attendants (FAs) said aircraft was hot; we started APU right away and put packs on high flow. FAs also advised they put hot aircraft in Company app and that the station decided to board. On taxi out started both engines right away on push back. Got to the runway and waited on final weights. Customer service was having issues finalizing the passenger count. Ground Control instructed us to park in the Runway XXR run up pad while waiting. Sent several ACARS requests for late weights and notified ops and load planning. After 5 mins of waiting for weights in the pad Flight Attendants notified of the delay via the cabin phone; and a passenger PA was made. No mention of cabin temp made by the Flight Attendants at this time. After 20 more minutes still trying to get final weights (load planning and ops were aware of the delay getting weights) the Flight Attendants called the flight deck; said that all 4 Flight Attendants were feeling sick and requested to go back to the gate. We were then informed that the cabin temp was hot and made them sick. All cabin zone temps were on cold; and all zone supply duct temp reading 20C. When the pass cabin temp was checked both fwd and aft read 40C. We immediately put packs on high and asked for a gate return. Flight deck was a comfortable temp and we had no communication of the cabin being hot after door closure prior to this phone call.Coordinated a gate return with ops and notified dispatch. Told to return to Gate XX.Upon taxi to the gate Flight Attendants notified us several passengers were feeling sick. Prior to turning into the ramp area for the gate the flight attendants called and said there was a sick passenger laying on the galley floor who could not stand up due to feeling faint and dizzy. Flight attendants requested medical personnel meet the flight. Ops notified we needed medical personnel. Waited for approx 10 more mins at in the ramp area at the lead in line for Gate XX for marshalers to come out. Notified ops multiple times we needed ramp agents. All passengers deplaned upon arrival at the gate. Medical personnel met the flight. 4 FAs and 1 passenger (that's all I know of) screened by medical personnel. To my knowledge no passengers received medical assistance beyond a gate screening. Maintenance write up made for cabin temp not controllable; and Maintenance decided to take the aircraft out of service. All Flight attendants recrewed due to feeling sick; and pilots recrewed due to aircraft swap that would exceed our Critical Crew Off time (CCO) time. Upon block in I notified Chief Pilot of the situation; and an in flight supervisor met the aircraft to assist the Flight Attendants.