B737-800
Flight Crew Air Transport Pilot (ATP)
Time Pressure; Other / Unknown
Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural MEL / CDL
Flight Crew Became Reoriented
Procedure; Aircraft; Human Factors; MEL
Aircraft flew in with 2 placards:  21-1 (for the Right Pack) and 21-16b (Flight Deck Temperature Control System).  We reviewed the MEL and verified that the placarding was done correctly and that we would be following proper procedures.  There were widespread thunderstorms along our planned route; thus the primary focus of my preflight planning was on the altitude restriction of FL250 due to MEL 21-1. While we were on the gate; the cabin was a little warm; but not above the point that would have prevented boarding.  But after takeoff; the cabin became very warm and the cockpit very cold.  During the entire flight we were only marginally successful in mitigating the comfort level on the aircraft. We were well into the flight; having spent a great deal of time assessing the situation before we came upon the root cause:  Under the MEL 21-16b; there is a note that primarily addresses flight deck temperature control.  But when combined with MEL 21-1 this ultimately meant that we were flying an aircraft with no temperature control at all.  While I reviewed the MEL while we were on the gate; I did not make the connection between this note and the placarding of the right pack. Because 21-16b is entitled 'Flight Deck Temp Control' it did not occur to me that we would have temperature control issues throughout the airplane and not just an issue of a constant 75 degree flow to the cockpit.  I did not draw the connection between the note at the end of MEL 21-16b and MEL 21-1. In retrospect; I should have refused this aircraft.  The MEL should be revised to make MELs 21-1 and 21-16b mutually exclusive.
B737-800 Captain reports being unable to control the cabin temperature after being dispatched with MEL's for the right pack and Flight Deck Temperature Control System inoperative. A condition for the Flight Deck Temperature Control inoperative MEL is that the right pack must be operational.