B737 AT FL370 EXPERIENCED HYD PROB; REQUESTED LOWER ALT AND DIRECT ROUTING PROMPTING NUMEROUS ATC QUESTIONS.

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SIT: HYD B SYS ENG DRIVEN PUMP LOW PRESSURE LIGHT ILLUMINATED. PRESSURE GAUGE INDICATING NORMAL. FO FLYING. APPROX 250 NM FROM ZZZ. ACTIONS: AS THE PNF; I READ THE QRH AND FOLLOWED THE PROCS (SHUT OFF THE PUMP). I ALSO MENTIONED THAT SOME TIME AGO I'D READ SOMETHING ABOUT THIS HAPPENING ON THE LONG HAUL FLTS WITH THE -700 AND IT HAD SOMETHING TO DO WITH A SENSOR GETTING REAL COLD AND SENDING AN ERRONEOUS SIGNAL. WITH THAT IN MIND; WE ASKED ATC FOR A LOWER ALT. IN THE MEANTIME; AS I PREPARED SO I COULD CONTACT DISPATCH AND MAINT; THE FO MENTIONED MAYBE WE OUGHT TO ASK FOR DIRECT ZZZ. WE REQUESTED EXPEDITIOUS ROUTING TO ZZZ AND CTR ACCOMMODATED US AND FURTHER ASKED US IF WE WERE DECLARING AN EMER TO WHICH WE RESPONDED 'NO.' (AFTER THAT; EVERY CTLR ASKED; 'ARE YOU DECLARING AN EMER?' TO WHICH WE CONSISTENTLY ANSWERED 'NO.') AS I WAS SETTING UP THE OBSERVER PANEL TO USE THE PHONE; THE FO TOOK THE #1 RADIO (ATC) AND TOLD THEM NEGATIVE; NO EMER; SOON THEREAFTER; THE HYD A SYS ENG DRIVEN PUMP LOW PRESSURE LIGHT ALSO ILLUMINATED. I RAN THE QRH CHKLIST ONCE MORE. IN THE MEANTIME; ATC QUERIED US AS TO WHAT KIND OF PROB WERE WE HAVING. I RESPONDED BY TELLING THEM THAT WE WERE SORTING IT OUT (WHICH WAS INDEED THE TRUTH). I THEN CONFERRED WITH DISPATCH AND MAINT AND PLANNED TO PROCEED TO OUR DEST; ZZZ (A MAINT BASE). WE CONTINUED TO ZZZ WITH A FEELING THAT THE SIT WAS MOST LIKELY ALT/TEMP/DURATION OF FLT RELATED; AS ADVERTISED IN THAT LITERATURE MENTIONED EARLIER. ALL THE WHILE; THE A AND B SYS HYD PRESSURE GAUGES HAD NOT WAVERED WITH PRESSURE INDICATING NORMAL. HOWEVER; SINCE WE HAD THE TIME; I DID REVIEW WITH THE FO WHAT FLT CTLS WERE AFFECTED WITH THE LOSS OF EITHER A OR B ENTIRELY AND LEFT THE QRH OPEN TO THE 'MANUAL REVERSION' PAGE (LOSS OF BOTH SYS). WHEN ANOTHER CTLR ASKED US WHAT OUR PROB WAS; I WAS THEN ABLE TO TELL HIM IT WAS A HYD SYS INDICATION; BUT THAT WE WERE PLANNING A NORMAL APCH AND LNDG AT ZZZ.