A CORPORATE JET ENTERED THE TOP OF A TRW AND WAS UNABLE TO CONTROL ALT; CLBING 1400 FT ABOVE CLRNC ALT.

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TOOK OFF FROM LUK. RADAR VECTORS ON DEP. AFTER HANDOFF FROM DEP TO CLEVELAND CTR; WE WERE CLRED TO 13000 FT. THEN TOLD TO MAINTAIN 12000 FT. WE WERE BEING VECTORED DIRECTLY AT A LINE OF CUMULUS CLOUDS. WE WERE RE-CLRED TO 13000 FT AS WE ENTERED THE RAPIDLY BUILDING CUMULUS CLOUDS. TURB INSIDE THE CLOUDS WAS LIGHT WITH ONE OR TWO MODERATE BUMPS. WE EXPERIENCED A RAPID CLB WITH AIRSPD INCREASING. I TRIED TO STOP THE CLB WITH FORWARD YOKE PRESSURE AND MAINTAIN AIRSPD BY REDUCING POWER. THE RAPID CLB CONTINUED EVEN WITH A 2 DEG OR 3 DEG NOSE DOWN ATTITUDE. I WAS FINALLY ABLE TO STOP THE CLB AT ABOUT 14200 FT AS WE CAME OUT THE TOP OF THE CLOUDS. I STARTED A DSCNT TO 13000 FT; BUT WAS GIVEN A FURTHER CLB TO FL230. NO COMMENTS WERE MADE BY CTR. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: PLT STATED THAT THIS EVENT DID NOT INCLUDE TURB. THE CREW ENTERED THE TOP OF A BENIGN APPEARING CLOUD AND OVER A MATTER OF SEVERAL SECONDS THE SPD AND RATE OF CLB INCREASED. THE ENTIRE EVENT WAS APPROX 10 SECONDS AND THE ACFT CLBED AT ABOUT 4000 FT PER MINUTE. ATC MADE NO COMMENT TO THEM AND SIMPLY CLRED THEM TO A HIGHER ALT. THE CREW DID NOT RPT THE CLB TO ATC BECAUSE OF THE CLB CLRNC.