car no heat/overheating; normal temp and heat under heavy acceleration

I have a 94 v6 mustang and it drives fine for a little
bit sometimes (heat works) but inevitably I lose
heat and shortly after that, temp starts to rise. But,
if I put it to the floor,  about 75% of the time, it
cools down to normal and heat will work. It's very
short lived because in about a min or 2 it will
happen again. It happened 4 times when I tried
getting to work in a 7 mile span from my house. It
won't overheat at idle even though most of the
time it has no heat at idle ( it was checked in below
freezing temps after a drive cause that's the only
way of getting it up to temp). All that being said I
am just finishing up school for automotive
technician and I know it can't be thermostat due to
no heat issue. I have flushed the system twice and
bled air out at least 5 times. I don't think the heater
core being clogged would cause an overheating
issue
I'm leaving toward water pump and guess some or
all fins are worn/erroded. Has radiator and
thermostat replaced about 15k miles ago due to
overheating. No coolant in oil and vice versa. I do
have a lean code for bank 1 but only bank 1. I'm
lost and don't have a lot of money so all help would
be appreciated. Sorry such long description