PIPER 31 PLT UNKNOWINGLY ENTERED A TEMPORARY RESTR AREA DURING A CROSS COUNTRY VFR FLT.

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TODAY OCT/THU/01 AT APPROX XA45 LOCAL TIME I FILED AN IFR FLT PLAN OFF OF XXX WITH A DEP OF XB15. WE TRIED TO CALL APCH CTL AT YYY AND COULDN'T GET THEM; SO I DEP VFR AND THOUGHT I WOULD CALL THEM IN THE AIR. WE DECIDED TO CONTINUE VFR BECAUSE IT WAS SUCH A BEAUTIFUL DAY. I DID FOLLOW MY PRE PLANNED RTE. I HAD ASKED THE FSS. IF I WAS ALRIGHT WITH ZZZ AIRSPACE WHEN HE TOOK MY FLT PLAN AND HE SAID YES. I HAD NO REASON TO THINK OTHERWISE. NEARING ZZZ ON AIRWAY I DECIDED TO CALL WWW APCH AND WHEN I DID; HE TOLD ME I VIOLATED ZZZ AIRSPACE. HE SAW ME ON AIRWAY AT 6500 FT BUT SAID THAT I HAD BEEN IN THE SPECIAL RESTR/FIXED AIRSPACE. HE GAVE ME A PHONE NUMBER AND TOLD ME THAT WHEN I LANDED AT XYZ TO CALL HIS SUPVR; WHICH I DID. I CALLED AT APPROX XB55 AND TALKED TO MR X. HE POLITELY TOOK MY INFO AND TOLD ME THAT HE WAS SORRY BUT THAT I WAS VIOLATED AND THAT SOMEONE FROM THE FSDO WOULD CONTACT ME; HE DID SAY THAT THEY COULD TALK TO HIM ABOUT THIS OCCURRENCE LATER; AND THAT WAS THE END OF THE CONVERSATION. I THANKED HIM AND HUNG UP. THIS WAS A SIT WHERE I WAS TRYING TO DO THE RIGHT THING; BUT DID NOT HAVE ALL THE RIGHT INFO; AND I DID CALL WWW NEARING ZZZ. I FLY THAT AIRWAY VERY OFTEN NEVER HAVING A PROB VFR OR IFR.