Can a heater core be mounted on the fireside.

You'll be heating the engine which I think is plenty hot enough already. Besides, it already has a really really big heater core under the hood. It's called the radiator.

You need to have the heater core inside the heater box. That's where all the vent and mode doors are along with the passages and ducts. To do what you're trying to do, you'd have to shove the heater core down into the fresh air inlet. First of all, it won't fit, and second, there would be no way to block the heated air when the air conditioning is turned on.