Start temperatures are provided for a number of reasons, but with one basic underlying intent; prevent engine damage.
Temperature as reported in the cockpit may be sampled at a number of different locations, depending on the type of engine which you're operating. Exhaust Gas Temperature, Interstage Turbine Temperature, etc, are different ways of describing the same thing; the temperature at some point in the exhaust flow. The problem is that during an engine start, the temperatures at other parts of the engine may be substantially different...you may have a low temperature exhibited at the tailpipe or between turbine stages, whereas a very high temperature may be occuring inside the burner can or the turbine inlet. Without a direct means of identifying what that temperature is, then limiting the start temp to a lower value is one way of ensuring that components aren't damaged during the engine start.
A hung start is a good example. During a hung start, inadequate airflow is occuring through the engine. The flame isn't going where it's supposed to, and you can't be assured of adequate airflow protection through the burner can to keep the flame off the burner can walls...you may also be experiencing streaking or flame propogation beyond the can...which can cause damage to turbine inlet guide vanes or turbine blades downstream. The EGT, ITT, or TiT, by be indicating a low temperature, but you may have a very hot, raging fire going on upstream of the temperature probes. You may be experiencing engine damage and not even show a temperature which appears to be harmful.
The same can be true of a normal start. Depending on where the temperature probes are located, you may have already experienced catastrophic engine damage before the temperature ever reaches a point on the EGT or ITT or TiT indicator that might appear harmful.
Airflow through the engine, and the conduct of heat and gasses, isn't the same during the engine start sequence as it is when the engine is running in a stable fashion.
Many engines use multiple stage nozzles which open or increase fuel flow at various points in the start, in order to bring the fuel flow up in stages as increasing airflow is available in the burner can to help keep the flame off the burner can walls. This is a very crucial time for the engine, as excess fuel will create temperatures that won't necessarily register as high on the cockpit indications, but could still easily cook internal components. As no cockpit indication exists to warn of this damage beyond a low limited start temperature, your first indication might just be shedding a turbine blade or an uncontained fire outside the burner can. As a result, some engines (due to the placement of the thermocouples in the temperature indicating system) do have a start temp which is lower than the other operating temperatures.
You may also be thinking of start temperatures which are used for cutoff purposes. The actual start limit may be 1100 degrees, for example, but the engine may have a start cutoff limit of 600 degrees. The reason for this is that normally to prevent damage you must cut off fuel if the temperature approaches the 600 degree point...but the damage limit is considerably higher. You can cut off the fuel early, save the engine, and perform another start...but if the temp hits the start limit redline, then you've got a hot section inspection and teardown coming. The specifics for the relationships of these numbers should be spelled out exactly, or in general, in the maintenance publications for the powerplant in question.