We study the Hagedorn transition in the singlet sector of the simplest super-string bit model in the tensionless limit. The gauge group of our model is SU(N) and this transition takes place when N is infinite. We use orthogonality of group characters in order to calculate the partition function. At the Hagedorn temperature there is a change in the distribution of parameters that maximize this partition function. We conclude by devising a field-theoretic interpretation of the this phenomenon.