Finite N corrections to white hot string bits

String bit systems exhibit a Hagedorn transition in the N -> infinity limit. However, there is no phase transition when N is finite (but still large). We calculate two-loop, finite N corrections to the partition function in the low-temperature regime. The Haar measure in the singlet-restricted partition function contributes pieces to loop corrections that diverge as O(N) when summed over the mode numbers. We study how these divergent pieces cancel each other out when combined. The properly normalized two-loop corrections vanish as O(N-1) for all temperatures below the Hagedorn temperature. The coefficient of this 1/N dependence decreases with temperature and diverges at the Hagedorn pole.