Data are presented for the ($^{3}\mathrm{He}$, $t$) reaction at energies of 600 MeV, 1.2 GeV, and 2 GeV on targets $^{\mathrm{nat}}\mathrm{C}$, $^{54}\mathrm{Fe}$, and $^{89}\mathrm{Y}$. The low-excitation-energy regions of the spectra are dominated by isospin-spin excitations. Cross-section calculations in distorted-wave impulse approximation with parameters from $\mathrm{NN}$ data account reasonably well for the data. At 2-GeV bombarding energy a strong excitation of the $\ensuremath{\Delta}$ resonance is observed for all targets.