AIRSHIP CAUGHT THERMAL CONDITIONS AND ENTERED CLASS B AIRSPACE WITHOUT CLRNC.

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THE AIRSHIP IS PRIMARILY USED AS A CAMERA PLATFORM FOR NETWORK TELEVISION COVERAGE. I TOOK OFF AT XA30 FROM SDM; TRANSITIONED THROUGH IMPERIAL NAS CLASS D AIRSPACE; THEN TO HALSEY TWR VIA THE CORONADO BRIDGE AT 1400 FT MSL. RECEIVED A SQUAWK TO TRANSITION NWBOUND THROUGH SAN DIEGO BAY. I WAS THEN HANDED OFF TO LINDBERGH TWR AND GIVEN NEW SQUAWK CODE. TRANSITIONED SURFACE AREA OF CLASS B. RADAR SVC WAS TERMINATED. ONCE CLR OF SURFACE AREA OF CLASS B; I CONTACTED MIRAMAR TWR AND INFORMED THEM THAT I WAS OUTSIDE OF THEIR AIRSPACE REQUESTING TRANSITION TO THE EVENT AREA JUST ON THE EDGE OF THEIR CLASS D AIRSPACE. TOLD THEM THAT I WOULD BE OPERATING BTWN 1800 FT MSL AND 1400 FT MSL FOR COVERAGE OF EVENT. I PLANNED ON 1400 FT MSL FOR THE DAY'S 3 HRS OF COVERAGE AND STATED 1800 FT MSL BECAUSE AIRSHIPS ARE PRONE TO THERMALS IN THE AIR CURRENT ON INDICATED ALT MIGHT EXCEED REQUESTED. AT THAT TIME MIRAMAR NAS TWR TOLD ME TO SQUAWK VFR AND CONTACT SOCAL FOR FLT FOLLOWING. I STATED THAT VFR FLT FOLLOWING WAS NOT NECESSARY. I MONITORED THEIR TWR FREQ DURING THE EVENT AND I IN FACT DID GET CAUGHT IN A THERMAL AND CLBED TO AN INDICATED ALT OF 1800 FT MSL. THE FLOOR OF THE SAN DIEGO CLASS B OVER COVERAGE AREA IS 1500 FT MSL AND I FAILED TO RECOGNIZE THIS FACT; AND I SHOULD HAVE CONTACTED SOCAL ON 119.6. I FEEL THAT COMING FROM A MIL TWR THAT THE PHRASEOLOGY 'VFR FLT FOLLOWING' IS MISLEADING AND MIRAMAR TWR SHOULD HAVE SAID FOR 'RADAR SVCS IN THAT AREA CONTACT SOCAL FOR YOUR REQUESTED ALT AND INTENTIONS.