Why do you think the charger is "overheating"? In a practical sense,
if the charger isn't melting or smoking, then it is probably working as
designed.

Why do you think the new batteries are of the same "...design"? If they
were, then they wouldn't draw any more current from the charger (thus
making it run hotter) than the old batteries. Seems possible the new
battereis are, in fact, not of the same internal design. The cells may
use a slightly (or entirely) different chemistry and/or physical
construction, even though they have the same voltage and current
ratings. Over the past few years, battery technology has changed very
substantially, and many of the improvements have been aimed at
permitting faster charging. Another fact is that no two manufacturing
facilities make "NiCad" or "Ni-Mh" or "Lithium" cells exactly the same
way...even when building to the same specs. Finally: If the new
batteries require an "adaptor cord" to attach them to the old charger,
that is a pretty substantial hint that SOMETHING is rather different.

Bottom line: If the new batteries charge and then power the drill, use
them until they fail to do so.