AN HS125 ON A POST MAINT TEST FLT EXPERIENCED AN ENG FUEL OVERHEAT; A TRIM IMBAL; AND A NON FUNCTIONAL AUTOPLT. AN EMER IS DECLARED.

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ACFT HAD JUST COME OUT OF AN 'E AND F' INSPECTION AS WELL AS LNDG GEAR OVERHAUL. MINOR PROBS NOTICED ON PREFLT AND WERE CORRECTED BY MAINT STAFF. AFTER TKOF; COPLT NOTICED ACFT WANTED TO ROLL R WITH ALL TRIMS CTR; BUT WE WERE ABLE TO CORRECT THIS PROB WITH MINOR TRIM CORRECTIONS. COPLT ENGAGED AUTOPLT AND I NOTICED THE XFER SWITCH NOT ENGAGED TO SWITCH AUTOPLT TO HIS SIDE. I ENGAGED XFER SWITCH BUT AUTOPLT DIDN'T SEEM TO ENGAGE. I THEN NOTICED AILERON TRIM LIGHT ILLUMINATE; SO I AGAIN ADJUSTED TRIM TO TURN LIGHT OFF. BY THIS TIME WE WERE LEVELING AT 11000 FT; SINCE ACFT SEEMED TO HAVE AN AUTOPLT PROB. I TOLD THE COPLT I HAD THE ACFT TO SEE IF I COULD FEEL WHAT WAS GOING ON. I THEN RE-TRIMMED THE ACFT FOR LEVEL FLT; AND GAVE ACFT BACK TO COPLT. I THEN NOTICED WE HAD A L ENG FUEL OVERHEAT LIGHT ILLUMINATED. I PULLED THE CHKLIST AND ITEM #1 WAS TO REDUCE PWR ON AFFECTED ENG. SO PWR WAS REDUCED. I ADVISED ATC WE HAD A PROB AND NEEDED TO RETURN TO ZZZ. THEY ASKED WHAT THE NATURE OF PROB WAS; AND WE ADVISED NO EMER WAS DECLARED AT THIS TIME; BUT WE ADVISED WE MAY HAVE TO. ITEM #2 OF THE CHKLIST SAID IF LIGHT CONTINUED TO BE ILLUMINATED TO SHUT ENG DOWN. DUE TO THE SIT; I DIDN'T NOTICE THE TIME FROM PWR TILL THE TIME I DECIDED WE NEEDED TO SHUT DOWN THE ENG BECAUSE THE LIGHT WAS STILL ON. WE THEN DECLARED AN EMER; AND JUST AS MY COPLT WAS REACHING FOR THE FUEL CUT-OFF; THE LIGHT WENT OUT. I ADVISED HIM SINCE THE LIGHT WAS OUT; WE WOULD LEAVE THE ENG RUNNING AT IDLE. ADVISED ATC WE DIDN'T SHUT DOWN ENG BUT WOULD STILL KEEP EMER STATUS. GIVEN VECTOR TO BASE LEG AT ZZZ AND TO FOLLOW TFC AT 11 O'CLOCK POS AND MAINTAIN 170 KTS. COPLT DIALED IN ILS FOR RWY 25L AND I NOTICED THAT I HAD DSNDED BELOW GS; SO BEGAN CORRECTING; BUT SPD HAD REDUCED TO ABOUT 140 KTS; CAPTURED GS; AND REGAINED SPD AND LANDED WITHOUT FURTHER PROBS. AFTER LNDG; SHUT DOWN L ENG. THINGS THAT WE COULD HAVE DONE DIFFERENT ARE: AFTER ACFT COMES OUT OF MAINT; I WILL NOW DO THE TKOF MYSELF RATHER THAN COPLT SO I GET THE FEEL OF WHAT IS GOING ON WITH ACFT. WHEN TOLD TO FOLLOW THE PREVIOUS TFC; I ALLOWED MYSELF TO BE DISTR OUTSIDE ACFT AND ALLOWED MYSELF TO DSND EARLY; THEN HAD TO CORRECT FOR ALT LOST; THUS SLOWING THE ACFT BELOW 170 KTS.