A control system is provided to effect a method to control torque output from a two-mode, compound-split, electro-mechanical transmission during gear-to-gear shifting event when an off-going torque-transfer device is disengaged. It includes a computer program which controls transmission operation. A predetermined preferred torque output from the transmission device is determined. Torque output from torque-generative devices device is controlled. Torque transmitted across a selectively actuated torque transfer device is controlled, and limited based upon available battery power. Actuation of the oncoming torque-transfer device is preferably based upon a temperature of the device during the shifting event. The temperature during the shifting event is determined based upon a rotational speedof an input shaft to the transmission and an elapsed time to shift.