Abstract: At the point of time to when the turbine speed has come up to a first speed N.sub.1, a thermal stress expected in the turbine when the speed is increased to a second speed N.sub.2 at a rate .alpha..sub.1 is presumed. Thermal stress .sigma..sub.s(t) -.sigma..sub.sT1 at the point of time t.sub.o1 for commencing acceleration to the second speed N.sub.2 is then obtained, which point of time t.sub.o1 would never cause the maximum value of the presumed thermal stress to exceed a predetermined limit .sigma..sub.sl of the thermal stress when the turbine speed is increased at that rate. Then, a length of time T.sub.w1, referred to as a warming time, is determined which is required for the thermal stress .sigma..sub.s(t) to decrease to the level of (.sigma..sub.s(t) -.sigma..sub.sT1) when the warming is continued after the point of time t.sub.o. Subsequently, a length of time (N.sub.2 -N.sub.1)/.alpha..sub.1 required for increasing the turbine speed from N.sub.1 to N.sub.2 at the rate .alpha..sub.1 is calculated.