Block copolymer materials can be aligned using shear forces; in order to fully exploit this phenomenon for controlling nanoscale order, the coupling between applied forces and molecular properties must be elucidated. We use a photothermal method to generate extreme and controllable thermal and stress fields in thin films of cylinder-forming block copolymers. By studying morphological ordering as a function of time, shear rate, polymer material, molecular weight, and film thickness, we elucidate the critical parameters with respect to efficient ordering. We find that ordering efficiency depends weakly on the block copolymer interaction parameter and strongly on the difference in mechanical response of the two phases. Morphologies can be aligned only when the inverse shear rate is smaller than the material's relaxation time. Overall, photothermal shear alignment provides an efficient means of ordering and aligning nanoscale morphologies over macroscopic areas, using a surprisingly short (subsecond) shear pulse.