C560 CREW LOST CABIN PRESSURIZATION AT FL420.

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WE WERE LEVEL FLT AT FL430. (ACTUALLY; WE WERE AT A BLOCK ALT FL410-FL430). WE HEARD A LOUD 'POP' AND RUSHING AIR. WE DONNED OUR OXYGEN MASKS; AND STARTED A DSCNT. THE EMER PRESSURE WAS ON AND IT TOOK US 1-2 MINS TO FIGURE OUT WHAT THE PROB WAS. WE COULD NOT COMMUNICATE VERY WELL WITH EACH OTHER OR WITH ATC DUE TO CIRCUMSTANCES BEYOND OUR CTL. AS WE PASSED THROUGH FL404; I HEARD ATC CLR AN AIRLINE TO A LOWER ALT BECAUSE OF OUR DSCNT. WHEN I FINALLY CONTACTED ATC; THEY CLRED US TO FL350. THE PROB WAS AN AIR CYCLE MACHINE OVERTEMP. WE CORRECTED IT AND CONTINUED WITH NO FURTHER PROBS. THE PROB WAS CAUSED BY HIGH ALT; LOW AIRSPD AND HIGH PWR SETTINGS WHILE ASKING THE AIR CYCLE MACHINE FOR COOLER AIR. A GOOD LESSON WAS LEARNED WITH NO HARM AND DUE TO ATC'S EXCELLENT WORK WE WERE ABLE TO CONTINUE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE ACFT IS CERTIFIED TO OPERATE TO A MAX ALT OF FL450. ACFT IS EQUIPPED WITH A SINGLE AIR CYCLE MACHINE OR 'PACK.' THERE IS NO REDUNDANCY. WHEN THE PACK TRIPS; AN AUTOMATIC SHUTDOWN OCCURS. THIS TRIP-OFF CANNOT BE OVERRIDDEN. AT THIS POINT; THE ACFT STARTS TO DEPRESSURIZE. THERE IS AN 'EMER PRESSURE VALVE' WHICH CAN BE OPENED. THIS DUMPS RAW ENG PNEUMATIC SYS AIR DIRECTLY INTO THE CABIN. PNEUMATIC SYS TEMP IS TYPICALLY 195 DEGS C. THERE IS NO COCKPIT TEMP INDICATION SO THE PACK TEMPS CANNOT BE MONITORED IN THE COCKPIT. THE CREW IS NOT ABLE TO SEE AN OVERTEMP TRIP-OFF COMING UP. PACK TRIPS HAVE BEEN A CONTINUING PROB FOR THE ACFT. CESSNA HAS INCLUDED A WARNING IN THE FLT MANUAL DESCRIBING THE PROB. THEY DON'T; HOWEVER; SAY WHAT TO DO ABOUT IT. THE PLT THINKS THAT THE AIR CONDITIONING AND PRESSURIZATION SYS SHOULD OPERATE RELIABLY THROUGHOUT THE OPERATING ENVELOPE OF THE ACFT.