Quite dilute CTAC/NaSal surfactant solution system (0.78-3.13 mmol/L) has been investigated with increasing temperature under shear for the first time. The experimental temperature range is very wide (10-60 degrees C) and astride the Krafft point (T-K). Even at a temperature 8 degrees C lower than T-K, the solution can remain in a transparent and homogeneous metastable state, due to the temperature-induced formation of higher ordered self-assemblies. Different shear rates induce very different assembly transitions for the same solution with same temperature increasing rate (r). A special "two peaks" phenomenon appears under the following conditions: concentration of 1.25-2.50 mmol/L, shear rate of 5 s(-1) and r of 0.0033-0.0333 degrees C/s. An equation is established to describe the relations between the change in rodlike micelle size with time (dR/dt) and the combined effects of shear and temperature. It can be found that either effect of shear or temperature has two aspects on dR/dt, therefore, the micellar size actually depends on the "matching-degree" of the two effects under our experimental conditions. Besides, the total free energy change in the surfactant solution system is analyzed to study the simultaneous effects of shear and temperature from energy viewpoint.