  We show that the bosonic sector of the $N=(1,0),\, 6D$ Salam-Sezgin gauged
supergravity model possesses a $T$-duality symmetry upon a circle reduction to
$D=5$. We then construct a simple magnetic rotating string solution with two
equal angular momenta. Applying the $T$-duality transformation to this
solution, we obtain the general boosted rotating dyonic black string solutions
whose global structures and thermodynamic quantities are also analyzed. Owing
to the fact that the solutions are not asymptotically flat, we find that there
are two distinct globally-different non-extremal solutions with two different
sets of thermal dynamic variables, with both satisfying the thermodynamic first
law and the corresponding Small relations. However, their BPS limit becomes the
same and we show that it preserves one quarter of supersymmetry by directly
solving the corresponding Killing spinor equations.
