fuel pressure
Keep in mind that I am just guessing from the other side of the US. Whether the pump is new or not, it is still subject to the effect of trash (the smallest shred). I read your other post and you suggest that there is no trash in the tank. None the less, the way the diaphragm pump works involves two valves that function in a one way flow manner. If anything gets in those valves (either one) the pump will not build adequate pressure to feed the pump as it should. I suggest that you install a primary fuel pressure gauge and with that, you can begin to eliminate what ISN'T wrong. I know that we all begin with a guess and a stab in the direction that we last were succesful. Correct diagnosis requires that we start and proceed with known points. Without guages, you have no known reference.
You mention night and day as well as cool and hot days. These factors may or may not have anything to do with the problem. But like you, I have had similar problems that seemed to manifest with wierd correlation. For instance? My 92 automatic would drop OD in and out till I wanted to shoot it when I drove toward the west. The further west I got the worse it would hunt in and out with the OD. By the time I got to Texas, I simply had no OD. The closer I got back to Georgia, the better it worked. I finally aborted the TPS and have a toggle switch on the shifter. I never could make the Dodge system work.
So when you know with out doubt that the pump is getting consistent fuel delivery at the input, if the problem still exist, you can say that the problem is inside the pump. Pull it and take it to a repair facility. With the right test equipment, they can duplicate hot operation conditions.
If you plumb in a direct reading guage, remember that you run the risk of fuel leak into the cab. Nasty Nasty Nasty. Use a sender and remote guage setup.
Best of luck.
James