The X1/9 uses basically the entire front end from a 128 transferred to the rear of the X1/9 - right down to the brakes, struts, etc. The transaxle is "conventional", as in, separate from the engine assembly - not unitized like a SAAB 99/900.
X1/9s should NEVER overheat - provided that the head gasket is intact and not leaking, the water pump is in good shape and the radiator not plugged. The long pipe run from the motor to the radiator takes care of half the heat transfer, so the radiator is underused, really.
Like all Italian cars, take care to keep the head bolts torqued correctly, and you won't have blown head gasket problems. The 1290 motor is the best of the FIAT SOHC motors - with the right cam it'll rev cleanly to nearly 9grand and that's without radical profiles or multiple carbs. If you can find an older 128 with the 1116cc motor, snag it and use the intake and exhaust manifolds from it - they flow MUCH better. While the 1116 head has smaller combustion chambers (more compression), the ports are smaller, so don't use it. Just mildly deck the 1290 head instead.
Be easy on the tranny though - X1/9's have a tendacy to explode ring and pinions. No drag starts/sidestepping the clutch. And the synchros can be rather fragile, so speed shifting isn't recommended.