Another interpretation of the Hagedorn temperature

Decay rates of massive open strings are investigated at finite temperature. Employing the approximation method of Mitchell, Sundborg, and Turok, another meaning of the Hagedorn temperature for the open string theory is clarified: It is the limiting temperature where the picture of splitting probability per unit length is violated. Below the Hagedorn temperature the decay rates have the same values as in the zero-temperature system. Explicit numerical evaluations support our analysis.