AN ALTDEV EXCURSION MADE DURING A LOSS OF AIRSPD AND AN APCH TO STALL BY A B737-700 AT FL390 ON FREQ WITH ZID; IN.

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ABOUT 2.5 HRS INTO OUR FLT; FO REQUESTED TO USE THE RESTROOM. I AGREED. IT WAS THE FO'S LEG. HE HAD MADE MENTION TWICE THAT THE AIRSPD CTL WAS A CHALLENGE DURING THIS FIRST PORTION OF THE 6 HR LEG. THE ACFT WAS STABLE AND WITHIN AN ACCEPTABLE SPD RANGE AS THE FO LEFT THE FLT DECK (REF TIME/SECURITY REF DOOR PINNING). I WAS ALSO BUSY WITH THE RTE ON THE RELEASE AND STUDYING THE RTE SEGMENT BREAKDOWN. I SOON NOTICED A SUBTLE BUFFET AND DIRECTED ALL MY ATTN TO THE BUFFET TO ADJUST THE PWR AS NEEDED. WE HAD MADE CONSTANT ADJUSTMENTS SINCE AT CRUISE ALT THERE HAD BEEN CONSTANT INTERMITTENT LIGHT CHOP. AT THE TIME OF THE OCCURRENCE THE RIDE WAS RELATIVELY SMOOTH. INITIALLY; I NOTICED THE AIRSPD WAS ONCE AGAIN VARYING FROM TARGET SPD. THE SPD DECREASED AS MUCH AS 20-25 KTS IN A SHORT MOMENT AT WHICH TIME I CHKED THE ENG GAUGES TO MAKE CERTAIN ALL WAS NORMAL. THE SPD CHANGE MADE ME THINK SOMETHING WAS NON NORMAL. AFTER A BRIEF ASSESSMENT OF ALL INSTS; I REALIZED THE SPD WAS CONTINUING TO DECREASE. PITCH WAS INCREASING. I DECIDED TO DISENGAGE THE AUTOPLT TO BE ABLE TO FEEL THE ACFT AND INITIATE THE RECOVERY. ONCE I HAD THE ACFT IN MY HANDS; I COULD TELL IT WAS APCHING A LOW SPD BUFFET. I STARTED A SHALLOW DSCNT RATE OF ABOUT 300-400 FPM AND CONTACTED CTR AND STATED I HAD ENCOUNTERED A BURBLE OF TURB AND NEEDED TO DSND NOW. THE CTLR ASKED TO WHAT ALT. I RESPONDED FL350. HE THEN CLRED ME TO FL350. I HAD ALREADY APPLIED CLB THRUST TO ASSIST IN THE SPD RECOVERY. I DON'T REMEMBER ANY MORE SAID FROM THE CTLR. THE DSCNT RATE WAS STILL SHALLOW. I CONTINUED THE DSCNT EVEN THOUGH I HAD A SATISFACTORY RECOVERY TO NORMAL FLT CHARACTERISTICS. (FO RETURNS.) WITH EVERYTHING BACK TO NORMAL; I REQUESTED TO BE CLRED BACK UP TO FL390. THE CTLR CLRED US TO FL390. NOTHING MORE WAS SAID BY THE CTLR. DURING THE CLB; I RE-ENGAGED THE AUTOPLT AND GAVE THE ACFT BACK TO THE FO. A FREQ CHANGE TO ZKC WAS RECEIVED AND WE MADE THE CHANGEOVER (CONTACTED IND QUALITY ASSURANCE -- NOT RESEARCHED YET). I TOLD HIM THAT THIS SMALL PART OF THE WHOLE OCCURRENCE MADE IT SOUND LIKE AN ALTDEV; BUT THAT I HAD REQUESTED FL350 AND WAS CLRED TO THAT ALT BY THE CTLR. HE JUST REPLIED THAT HE HAD NOT YET RESEARCHED THE INCIDENT. HE TOOK MY NAME AND PHONE NUMBER. HE SUGGESTED THAT I MAKE NOTES FOR FUTURE REF. COMMENTS: IT WAS OBVIOUS THAT THE ACFT GOT INTO THE LOW SPD BUFFET RANGE AND WAS VERY SENSITIVE ON THE CTLS. THERE WAS A GROUP OF DISTRS SURROUNDING THE FO LEAVING THE COCKPIT DUE TO THE REQUIRED SECURITY MEASURES. AIRSPD CTL HAD BEEN IN NEED OF CONSTANT ATTN FOR QUITE A WHILE WITH THE FO MAKING MANY THROTTLE POS CHANGES. I NOTICED A MAJOR TEMP CHANGE OF ALMOST 10 DEGS ABOUT THE TIME OF THE OCCURRENCE. WE ALSO HIT A PATCH OF LIGHT TURB WITH THE TEMP DEV. I ANTICIPATED THAT THE FO HAD ADJUSTED THE PWR DOWN SLIGHTLY TO COMPENSATE FOR A SPD INCREASE JUST PRIOR TO LEAVING THE COCKPIT. THE PERFORMANCE COMPUTER WAS CHKED ONCE THE FO WAS BACK IN HIS SEAT TO COMPARE THE PRESENT CONDITIONS TO THE PERFORMANCE WE EXPERIENCED. WE DID HIT THE LOW END OF THE SPD RANGE. THE CDU SHOWED THE MAX CRUISE ALT TO BE FL398 AT THE TIME OF THE OCCURRENCE. THE PWR WAS SET FOR MAX CLB BUT THE ACCELERATION WAS VERY SLOW AT WHICH POINT I DECIDED TO START THE DSCNT TO EXPEDITE THE RECOVERY AND PREVENT ANY FURTHER DEGRADATION OF SPD. THE IOE WAS A SLIGHT FACTOR DUE TO LACK OF EXPERIENCE ON THE FO SIDE; HOWEVER; WAS NOT THE CAUSE; IN MY OPINION. THE DISPATCH RELEASE SHOWED THE LARGE TEMP DEV ALONG THE RTE ABOUT THE AREA WE EXPERIENCED THE OCCURRENCE. ATC NEVER INDICATED THAT THERE WAS A PROB WITH THE OCCURRENCE. SUPPLEMENTAL INFO FROM ACN 538651: CAPT ASKED FOR A PHONE NUMBER TO FOLLOW UP. CAPT CALLED ARTCC AND WAS NOTIFIED THAT SOME INVESTIGATION IS BEING MADE.