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Bosonic boundary states at finite temperature are constructed as solutions ofboundary conditions at $T\neq 0$ for bosonic open strings with a constant gaugefield $F_{ab}$ coupled to the boundary. The construction is done in theframework of thermo field dynamics where a thermal Bogoliubov transformationmaps states and operators to finite temperature. Boundary states are given interms of states from the direct product space between the Fock space of theclosed string and another identical copy of it. By analogy with zerotemperature, the boundary states heve the interpretation of $Dp$-brane atfinite temperature. The boundary conditions admit two different solutions. Theentropy of the closed string in a $Dp$-brane state is computed and analysed. Itis interpreted as the entropy of the $Dp$-brane at finite temperature.Comment: 21 pages, Latex, revised version with minor corrections and  references added, to be published in Phys. Rev.

Bosonic D-branes at finite temperature with an external field