  The appearance of space/time non-commutativity in theories of open strings
with a constant non-diagonal background metric is considered. We show that,
even if the space-time coordinates commute, when there is a metric with a
time-space component, no electric field and the boundary condition along the
spatial direction is Dirichlet, a Moyal phase still arises in products of
vertex operators. The theory is in fact dual to the non-commutatitive open
string (NCOS) theory. The correct definition of the vertex operators for this
theory is provided. We study the system also in the presence of a $B$ field. We
consider the case in which the Dirichlet spatial direction is compactified and
analyze the effect of these background on the closed string spectrum. We then
heat up the system. We find that the Hagedorn temperature depends in a
non-extensive way on the parameters of the background and it is the same for
the closed and the open string sectors.
