COMMUTER SMT RWY EXCURSION. ACFT SLID OFF THE END OF THE RWY IN HEAVY RAIN.

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WE WERE PAINTING A TSTM CELL NW OF PADUCAH AIRFIELD ON THE RADAR. WE CONFERRED WITH ZME AS TO ITS DIRECTION AND WOULD WE BE ABLE TO LAND BEFORE IT ARRIVED AT THE ARPT? THEY SAID THAT THE CELL WAS MOVING SE; AND THAT WE SHOULD BE ABLE TO LAND BEFORE IT ARRIVED. THEY ADVISED ME THAT IT WOULD BE AN ILS 4 APCH AND HOW CLOSE COULD I TAKE THE TURN ON? I ADVISED THEM THAT AS CLOSE AS HE COULD TO THE OM WOULD BE FINE. APPROX 10 MI OUT FROM THE OM WE WERE STILL VFR HOWEVER THE CEILINGS WERE LOWERING; APPROX 5 MI OUT FROM THE OM WE ENCOUNTERED HEAVY RAIN AND MODERATE TURB. WE WERE TURNED ONTO THE ILS APPROX 3 MI OUT FROM THE OM AND TOLD TO MAINTAIN 2500 FT UNTIL ESTABLISHED; CLRED FOR THE APCH. THEN STABILIZED IN THE CORRECT CONFIGN WITH THE AIRSPD AT 140 KTS. DH ON THE APCH IS 610 FT WITH A VIS REQUIREMENT OF 1/2 MI. AT APPROX 800 FT THE F/O CALLED RWY IN SITE AND I STATED THAT I WAS GOING VISUAL. I COULD SEE THE APCH LIGHTS AND APPROX 3000 FT OF RWY. I CALLED FOR FULL FLAPS. TWR ADVISED ME THAT WIND WAS 340 WITH GUSTS TO 22 KTS; AND THAT VIS WAS 3/4 MI. MY SPD AT THIS TIME WAS APPROX 125 KTS (IE; VREF + 10/15). TOUCHDOWN WAS SMOOTH AND SPD WAS 107 KTS. ALLOWING FOR GUSTS AND SOME FLOAT DURING THE FLARE I WOULD ESTIMATE THAT THE TOUCHDOWN POINT WAS APPROX 2000-2500 FT DOWN THE RWY; ALLOWING ME 3000-4000 FT TO STOP THE ACFT. THE ACFT YAWED TO THE LEFT AND SLID SIDEWAYS TOWARD THE RIGHT SIDE OF THE RWY. THE ACFT WAS AQUAPLANING. WITH THE USE OF DIFFERENTIAL REVERSE I WAS ABLE TO ARREST THE SLIDE OFF THE RWY. HOWEVER WITH APPROX 1000 FT OF RWY REMAINING THERE WAS STILL NO BRAKING WHATSOEVER. I ESTIMATE THAT THE ACFT SPD WAS LESS THAN 50 KTS WHEN IT LEFT THE RWY IN A CTLED STATE; AND EVENTUALLY CAME TO REST ON THE MUD OFF THE END OF THE RWY. I ADVISED THE TWR THAT THERE WAS NO APPARENT DAMAGE AND THAT THERE WERE NO INJURIES TO THE PAX; AND THAT WE WOULD NEED SOME ASSISTANCE TO TAKE THE PAX OFF THE ACFT. I THEN CALLED FOR AN AFTER LNDG CHKLIST; FOLLOWED BY THE ENG SHUT DOWN CHKLIST. THE CRASH CREW WERE PROMPTLY ON THE SCENE AND AFTER 10 MINS OR SO TRANSPORTATION ARRIVED FOR THE PAX. IN CONCLUSION: THIS WAS A NORMAL APCH WITH THE ACFT CORRECTLY CONFIGURED AS PER THE GOM. AT NO TIME DID WE DEVIATE FROM THE GOM OR FAR'S. TOUCHDOWN WAS NORMAL; BUT THEREAFTER THE ACFT STARTED TO AQUAPLANE. THIS WAS LATER CONFIRMED BY EVIDENCE OF REVERTED RUBBER HYDROPLANING ON THE 4 MAIN TIRES. THE RWY HAS JUST RECENTLY WITHIN THE LAST 10 DAYS BEEN RESEALED; WITH THE WHITE LINING DONE IN THE LAST 3 DAYS. AFTER THE INCIDENT WHILST WALKING THE RWY; THE SURFACE WAS FOUND TO STILL BE VERY SLIPPERY. DURING THE APCH THERE WERE NO RPTS OF STANDING WATER OR BRAKING ACTION GIVEN BY THE TWR. A SUBSEQUENT MAINT INSPECTION OF THE ACFT RPTED NO DAMAGE TO THE AIRFRAME; ENGS; PROPS; OR LNDG GEAR. ONLY THE TIRES WHICH HAD CLEAR EVIDENCE OF HYDROPLANING.