THE PLTS WERE PRACTICING LNDGS, AND WERE ON THE 3RD FLT AFTER THE ENG HAD BEEN OVERHAULED. AFTER TAKEOFF FROM A TOUGH-&-GO, THE INSTRUCTOR NOTICED THAT THE OIL TEMP WAS HIGH. SOON THEREAFTER, THE ENG BEGAN TO RUN ROUGH, THEN IT SEIZED. UNABLE TO GET BACK TO THE RWY, HE LANED IN A PLOWED FLD. HE SAID HE INTENDED TO LND WITH THE GEAR RETRACTED, BUT THE ACFT TOUCHED DOWN WITH THE GEAR EXTDD, THEN BOUNCED & NOSED OVR. THE CFI BELIEVED THE STUDENT MAY HAVE EXTDD THE GEAR, JUST BFR LNDG. INV REVEALED A CATASTROPHIC INTERNAL FAILURE OF THE ENG HAD OCCURRED. THERE WAS EVIDENCE OF AN OVERSPEED. A WITNESS RPRTD THAT DUE TO IMPROPER INSTLN OF THE CARB THROTTLE ARM, THE ENG WENT TO FULL PWR, WHEN IT WAS STARTED AFTER OVERHAUL. RPRTDLY, IT STAYED AT FULL PWR FOR SVRL MIN BFR IT COULD BE SHUT DOWN. A TEARDOWN REVEALED THE CONNECTING RODS HAD FAILED, THE CYL SKIRTS WERE DMGD, 1 PISTON WAS DESTROYED & OTRS WERE DMGD, SVRL BEARINGS WERE WORN & OVERHEATED, METAL CHIPS/CONTAMINATION FND IN ENG & OIL SYS. ENG HAD BEEN OPERD ABOUT 7 HRS SINCE OVERHAUL.