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.