  We consider the N_f-flavour Schwinger Model on a thermal cylinder of
circumference $\beta=1/T$ 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
$\theta$ 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 $L \to \infty$ 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 $\delta$ the numerical value is found to be
2 which is at variance with their bosonization-rule based prediction
$\delta=3$.
