PA38 INSTRUCTOR AND STUDENT HAD AN NMAC WITH A J-3 AT T65.

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ON A VFR TRAINING FLT IN A PA38 TOMAHAWK; GREAT WX. WE HAD ENTERED THE PATTERN; DONE A TOUCH AND GO; AND REMAINED IN THE PATTERN TO A FINAL. SINCE THIS WAS A TRAINING FLT; I MADE SURE THAT PROPER COM CALLS WERE MADE AT THE UNCTLED ARPT (T-65; WESLACO-MID VALLEY; TX). AS WE TURNED BASE TO FINAL BOTH THE STUDENT AND I NOTICED A PIPER CUB ON THE TXWY; ABOUT 1200-1500 FT FROM THE RUN-UP AREA FOR RWY 13. WIND WAS 120 DEGS AT 10 KTS. WE TURNED FINAL. WHILE ON SHORT FINAL; ABOUT 300 FT OR SO AGL THE CUB PASSED US GOING IN THE OPPOSITE DIRECTION AT THE SAME ALT; ABOUT 100 YDS ON OUR PORT SIDE. THERE WAS NO COM AT ALL FROM THE CUB; AND I DO NOT KNOW IF HE HAD A RADIO OR A HAND-HELD; AND ONE IS NOT REQUIRED FOR THAT AIRPLANE. THAT WAS THE FIRST TIME I SAW HIM AIRBORNE. HAD HE GONE TO HIS L ON TKOF THERE WOULD CERTAINLY HAVE BEEN A MIDAIR AS I DID NOT HAVE TIME TO REACT; ALTHOUGH I DID LAUNCH A BIG EXPLETIVE. IT WAS A CLASSIC PERIPHERAL VISION/BLOSSOM EFFECT NEAR MISS. THE ARPT IS A GOOD ONE; BUT DUE TO GENERALLY LIGHT TFC SOME PLTS TEND TO BE LAX. HIS MISTAKES ARE OBVIOUS: DOWNWIND TKOF ON A TXWY; NO COM; POOR SITUATIONAL AWARENESS; POOR SEE/AVOID PROCS; A DANGER TO OTHERS; AND A CANDIDATE FOR THE DARWIN AWARD. MY MISTAKES: I FAILED TO WATCH HIM ALL THE WAY. THE GOOD THINGS I DO: ON THE TURN FROM DOWNWIND TO BASE I TEACH THE STUDENTS TO DO A VISUAL SWEEP; AND AGAIN IMMEDIATELY PRIOR TO THE TURN FROM BASE TO FINAL. SPECIFICALLY WE LOOK AT THE LNDG ENVIRONMENT. WE DID SEE THE TAXIING AIRPLANE; BUT DID NOT CONTINUE TO VISUALLY TRACK HIM TO THE RUN-UP AREA. THIS INCIDENT DISTURBS ME; BUT IT PARTICULARLY DISTURBS ME THAT A STUDENT HAD TO SEE AN EXAMPLE OF POOR PLT DISCIPLINE. I SAW THE ARPT MGR AND RPTED THE INCIDENT.