  Bosonic boundary states at finite temperature are constructed as solutions of
boundary conditions at $T\neq 0$ for bosonic open strings with a constant gauge
field $F_{ab}$ coupled to the boundary. The construction is done in the
framework of thermo field dynamics where a thermal Bogoliubov transformation
maps states and operators to finite temperature. Boundary states are given in
terms of states from the direct product space between the Fock space of the
closed string and another identical copy of it. By analogy with zero
temperature, the boundary states heve the interpretation of $Dp$-brane at
finite temperature. The boundary conditions admit two different solutions. The
entropy of the closed string in a $Dp$-brane state is computed and analysed. It
is interpreted as the entropy of the $Dp$-brane at finite temperature.
