car spits sputters and misfires on fuel demand only when having reached operating temperature

when operatingb temp is reached the vehicle begins to act like it is either bogging down in a too high gear as they do or under demand for fuel it cuts out like starving for fuel.Also once it is at cruising speed about 2000 to 2400 rpm it starts to cut out too. Before it would remain running at idle and now it dies but this has been progressive after a weeksn driving in said condition.
Fuel filters checked and replaced as well as a gasket at the fuel pump where it seats on distributor shaft.