A DEPARTING C172 AT 3000 FT HAS AN NMAC WITH A CLBING C130 JUST SW OF TYS; TN.

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I WAS GIVING DUAL INSTRUCTION TO A STUDENT PLT IN HIS FIRST EXPERIENCE IN A CTLED FIELD. WE OBTAINED A VFR DEP CLRNC TO FLY HDG 250 DEGS AND CLB TO 4500 FT. THE WINDS WERE GUSTY AND THE STUDENT WAS HAVING DIFFICULTY HOLDING HDG. IN ADDITION; THE BUMPS MADE THE WET COMPASS ACT ERRATICALLY. TWR INSTRUCTED US TO FLY INITIAL HDG 230 DEGS AND CONTACT DEP. DEP CTL REPLIED; 'CLB TO REQUESTED ALT;' WHICH I INTERPED TO MEAN ON COURSE AS WELL. AFTER ABOUT 5 MINS; THE CTLR ASKED OUR HDG; WHICH WAS 235 DEGS AT THAT TIME; WHICH I TOLD ATC. THE STUDENT WAS HAVING TROUBLE ARRESTING THE L TURNING TENDENCY; AND EVEN THOUGH HE WAS ATTEMPTING TO FLY OUR CLRNC HDG OF 250 DEGS; WE WERE INDICATING 235 DEGS. ABOUT A MIN OR SO LATER; THE CTLR CALLED AGAIN ASKING OUR HDG; WHICH WAS STILL 235 DEGS. HE INDICATED OUR GND TRACK WAS 250 DEGS; WHICH DID NOT SURPRISE ME WITH THE STRONG WINDS; BUT HE NEVER TOLD US TO TURN OR FLY A NEW HDG; HE JUST SEEMED TO TAKE ISSUE WITH OUR INDICATED HDG. WHILE I CONTINUED TO PROVIDE HIM WITH THE INFO HE REQUESTED; I LOOKED DOWN AND SAW THE C130 PASSING QUICKLY UNDERNEATH AND TO THE R OF OUR PLANE. ATC THEN ADVISED ME OF THE C130 AND TOLD ME HE WAS 'CLBING THROUGH YOUR ALT.' I RESPONDED WE HAD THE TFC AND THAT IT WAS NO LONGER A FACTOR. HAD I KNOWN HE WAS COMING; I WOULD HAVE MADE SURE WE WERE WELL OUT OF HIS WAY. I WAS UNCLR AS TO WHICH HDG TO FLY BASED ON THE GIVEN CLRNC OF 250 DEGS AND LACK OF ANY ASSIGNED HDG BY DEP CTL. I BELIEVE COMS COULD HAVE BEEN BETTER BY ATC AND MYSELF.