  A calculation of the $^3$He transverse $(e,e')$ inclusive response function,
$R_T$, which includes $\Delta$ degrees of freedom is performed using the
Lorentz integral transform method. The resulting coupled equations are treated
in impulse approximation, where the $NNN$ and $NN\Delta$ channels are solved
separately. As NN and NNN potentials we use the Argonne V18 and UrbanaIX models
respectively. Electromagnetic currents include the $\Delta$-isobar currents,
one-body N-currents with relativistic corrections and two-body currents
consistent with the Argonne V18 potential. $R_T$ is calculated for the breakup
threshold region at momentum transfers near 900 MeV/c. Our results are similar
to those of Deltuva {\it et al.} in that large $\Delta$-isobar current
contributions are found. However we find that these are largely canceled by the
relativistic contribution from the one-body N-currents. Finally a comparison is
made between theoretical results and experimental data.
