This could be caused by a dirty fuel filter being plugged with debris. Another cause could be spark plug fouling or bad spark plug wires grounding out or cross firing.
Depending on year you should look at the EGR system or a tune up. On 87-95 trucks with TBI the EGR system has proven to be problematic and will cause surging at steady throttle. On 96 and newer the best thing to do would be a diagnostic scan.
Sounds as if it needs a tune up or some sensor is bad. Most parts stores can run a diagnositcs on it for free. Also try better grade gas, dry gas or carburator cleaner in gas.
The motor and tranny warm up, it starts to hesitate when triying to shift.. The tachometer and motor seem to stay steady when the problem occurs.. Could it be the torque converter,Pretty sure its not the trans it Had the trans fluid flushed and replaced about three months/ 5000 miles ago,may be oil has some dirt.
If your truck is hesitating at a steady speed it sounds like you might have some kind of fuel or air mixture problem. Anytime I see a hesitation problem it most likely tends to relate to this part of engine function.