Will my car overheat if I put a smaller radiator in it than the original a 97 Ford expedition XLT

What is your question?

I have recently we're place my thermostat water pump and radiator but the radiator that I put in the car it's not the same size as the radiator that came out and when I drive it and accelerate it is overheating and cooling is coming out of the cooling jug so what I wanted to know is is it overheating because I put a smaller radiator in it

What makes this problem better or worse?

It gets worse when I try to accelerate faster

How long has your 1997 Ford Expedition had this problem?

I have had this problem every since I changed the thermostat and put a smaller radiator into my 97 Ford expedition than the original radiator