We consider the N f -flavour Schwinger Model on a thermal cylinder of circumference ;=1ÂT and of finite spatial length L. On the boundaries x 1 =0 and x 1 =L the fields are subject to an element of a one-dimensional class of bag-inspired boundary conditions which depend on a real parameter % and break the axial flavour symmetry. For the cases N f =1 and N f =2 all integrals can be performed analytically. While general theorems do not allow for a nonzero critical temperature, the model is found to exhibit a quasi-phase-structure: For finite L the condensate seen as a function of log(T) stays almost constant up to a certain temperature (which depends on L), where it shows a sharp crossover to a value which is exponentially close to zero. In the limit L Ä the known behaviour for the one-flavour Schwinger model is reproduced. In case of two flavours direct pictorial evidence is given that the theory undergoes a phase-transition at T c =0. The latter is confirmed as predicted by Smilga and Verbaarschot to be of second order but for the critical exponent $ the numerical value is found to be 2 which is at variance with their bosonization-rule based result $=3.