A BE35 PLT WHILE TRYING TO AVOID WX INADVERTENTLY ENTERS A TFR.

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DEPARTED VERMILION COUNTY ARPT (DANVILLE; IL) ENRTE TO TULLAHOMA REGIONAL (TULLAHOMA; TN). THIS WAS SECOND LEG OF 2 LEG TRIP ORIGINATING AT OSHKOSH; WI. ENRTE STOP AT DANVILLE WAS MADE FOR FUEL AND WX UPDATE. FLT WAS BEING CONDUCTED VFR WITH FLT FOLLOWING. 2 SEPARATE BRIEFS HAD BEEN GIVEN BY FLT SVC PRIOR TO DEPARTING OSHKOSH. WHEN DEPARTING DANVILLE THE WX WAS VFR BUT APPEARED TO BE LOWER CEILINGS AND VISIBILITY TO THE S ON MY INTENDED COURSE. I DEVIATED E INTO WHAT APPEARED TO BE BETTER CONDITIONS. ONCE ESTABLISHED AND WITH THE DECISION MADE TO CONTINUE S ON MY RTE I WAS APPROX 25 MI NNE OF HULMAN INTL (TERRA HAUTE; IN) AND CONTACTED THEM TO INITIATE MY FLT FOLLOWING. THEY ADVISED ME I WAS JUST INSIDE A TFR AND GAVE ME A VECTOR TO EXIT THE AREA. THE CTLR ASKED IF I HAD OBTAINED A FLT BRIEF AND I ANSWERED IN THE AFFIRMATIVE BUT THAT NO MENTION HAD BEEN MADE ON EITHER OF THE 2 BRIEFS CONCERNING TFR'S. I WAS GIVEN A NUMBER TO CALL WHICH I DID UPON REACHING MY DEST APPROX 3 HRS LATER. THIS FLT WAS BEING CONDUCTED WITH RECOMMENDED VFR PROCS UTILIZING FLT FOLLOWING AND FAA BRIEFING SVCS.