Steve wrote:

I cut a hole in a wall to insert a 27"TV. The hole aligns with a stairway on
the other side. (about 8 steps.) So the Tv fits into the empty space under
the stairs. Its a split level house. One level in front and two levels in
the back. 1/2 set of stairs lead down and another 1/2 set of stairs lead up.

So the top of the stairs is about 4' above the base of the TV...

...I'm concerned with the heat generated by the TV causing the TV to overheat.

The cooler the better, but 80 F is probably OK.

There is a large closet next to the space that I can cut a hole through...
Would I be better to Pull air into the space and it would exit out the front
around the TV? Or should I turn the fan around and pull air out of the
space, sucking air in from around the front of the TV and blowing it into
the closet. ( the closet is always open. Its got louvered bi-fold doors).

I'd cut holes into the closet near the TV base and the top of the closet.

The opening around the TV is about 1/2" on each side and 2" on the top.

If the TV uses 150 W (512 Btu/h), a 512/10 = 50 cfm airflow would make
a 10 F temp rise from 70 to 80 F... 50 cfm = 16.6Asqr(4'x10F) makes
the vent area A = 0.47 ft^2, eg two 2'x3" slots.

Nick