The target space dependence of the Hagedorn temperature

The effect of certain simple backgrounds on the Hagedorn temperature in theories of closed strings is examined. The background of interest are constant Neveu-Schwarz $B$-fields, a constant offset of the space-time metric and a compactified spatial dimension. We find that the Hagedorn temperature of string theory depends on the parameters of the background. We comment on an interesting non-extensive feature of the Hagedorn transition, including a subtlety with decoupling of closed strings in the NCOS limit of open string theory and on the large radius limit of discrete light-cone quantized closed strings.