The 4T65E transmission features a "forward" clutch that is engaged in 1st gear forward only. Once it shifts into 2nd, this clutch is released. It is only applied in 1st. The inner piston seal gets worn or the piston area gets worn where the seal rides. What is happening is once you slow down and stop, the line pressure which is at minimum because the throttle isn't touched, fails to pressurize the clutch piston completely to engage the forward clutch plates. When you "tip in" or hit the throttle to take off, the line pressure jumps and builds enough pressure to apply the piston, thereby engaging the forward clutch. This is why the transmission hesitates or bumps into 1st gear on takeoff when hot. The complete remedy is to pull the transmission and do a total overhaul, replacing the parts that are worn in the forward clutch housing and a new improved inner piston seal. The other remedy is to manually downshift into 1st gear by using the transmission selector lever when coming to a stop. When you select low range with the shifter lever, the line pressure is raised from about 100psi to about 175psi which helps engage the forward clutch piston and overcomes the pressure leak on the inner piston seal.
Note that it also is possible that the EPC or (PCS) solenoid before mentioned can also cause this problem as the EPC solenoid sticks and doesn't regulate the line pressure to about 100psi when idling in drive. This can be verified by using a transmission pressure gauge and driving down the road while watching line pressure. If the line pressure is accurate, then the inner piston seal is the problem and not the EPC (electronic pressure control) solenoid.
Note that this forward clutch in the 4T65E is the same exact clutch that is used in the 440T4 transmission that was used for years without this problem. However with the 440T4 transmission, the forward clutch remained engaged in all "forward" ranges so this never developed into a problem.