You have posted your thread in the forum for "Valve engineering". I suggest that you move your thread to the "Engine & turbine engineering" forum.
In general, hot, warm and cold start-up conditions refer to the metal temperature of the rotor in the steam turbine HP (High Pressure) and/or IP (Intermediate Pressure) section. The range of temperatures for each type of start varies depending on the manufacturer of the turbine and the material of the rotor.
In some cases, the turbine manufacturer will correlate the type of start to the number of hours from the time that the steam turbine was shut down.
Since temperature of the rotor metal can not be measured directly, it is usually simulated by measuring metal temperature at an adjacent area in the turbine casing.
I hope this information was helpful.
Best of luck!