FALCON 50 FUEL FEEDER TANK INDICATED LOW FUEL. THE FLT CREW WAS UNCERTAIN AS TO THE CAUSE OF THE ANOMALY AND DIVERTED.

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WE WERE ENRTE FROM ZZZZ AT FL400. TAT OF -71 DEGS C. WE NOTICED THAT OUR #1 (L) FEEDER TANK WAS INDICATING ABOUT 200 LBS OF FUEL; INSTEAD OF 600 LBS. WE DISCUSSED IT AND RULED OUT A FUEL LEAK; WHILE I PULLED OUT THE ABNORMAL CHKLIST FOR THE SITUATION. WE WERE ABLE TO USE THE EMER FUEL XFER VALVE TO BRING THE FUEL LEVEL UP TO 600 LBS; WHERE IT REMAINED. WE FIGURED THE FLOAT VALVE FOR THAT TANK FROZE DUE TO THE -71 DEG C TAT; AND OUR 5+ HRS IN THE AIR. WE TRIED TO DSND INTO WARMER AIR; BUT COULDN'T; DUE TO TFC BELOW AND A LINE OF TSTMS MOVING OFF THE COAST. ONCE PAST THEM WE DECIDED TO LAND AT ZZZ. WE HAD BECOME PUZZLED BY WHAT SEEMED TO BE AN INDICATION OF LESS FUEL THAN WE THOUGHT WE SHOULD HAVE; AND THOUGHT IT BETTER TO FIGURE IT OUT ON THE GND. WHEN WE TOLD THAT TO ATC; THEY DECLARED AN EMER FOR US; SAYING NOT TO WORRY ABOUT ANY PAPERWORK. THEY JUST WANTED TO GIVE US PRIORITY. AFTER LNDG; THE FIRE DEPT CHKED FOR SIGNS OF FUEL LEAKING; AND FOUND NONE. WE WERE THERE ON THE GND OVER 4 HRS; WHILE WE HAD A MECH LOOK IT OVER. WE ALSO SPOKE TO A FALCON JET TECHNICAL REPRESENTATIVE; WHO AGREED THAT WE MOST LIKELY DID HAVE A FROZEN FLOAT VALVE IN THAT FEEDER TANK; AND THE FUEL XFER PROC SOLVED IT FOR US. HE ALSO POINTED OUT THAT FUELING IN ZZZZ; AT 90 DEGS F (FUEL TEMP WARM); THEN CLBING UP INTO SUPER COLD AIR AS WE DID; COULD RESULT IN A DIFFERENCE IN THE FUEL READING OF AS MUCH AS 400-500 LBS! WE DRAINED THE FUEL SUMPS; FUELED (WITH SOME WARMER FUEL); AND FLEW TO DEST WITHOUT INCIDENT.