We investigate the conditions under which parallel-propagating
Alfv\'en/ion-cyclotron (A/IC) waves and fast-magnetosonic/whistler (FM/W) waves
are driven unstable by the differential flow and temperature anisotropy of
alpha particles in the solar wind. We focus on the limit in which $w_{\parallel
\alpha} \gtrsim 0.25 v_{\mathrm A}$, where $w_{\parallel \alpha} $ is the
parallel alpha-particle thermal speed and $v_{\mathrm A}$ is the Alfv\'en
speed. We derive analytic expressions for the instability thresholds of these
waves, which show, e.g., how the minimum unstable alpha-particle beam speed
depends upon $w_{\parallel \alpha}/v_{\mathrm A}$, the degree of alpha-particle
temperature anisotropy, and the alpha-to-proton temperature ratio. We validate
our analytical results using numerical solutions to the full hot-plasma
dispersion relation. Consistent with previous work, we find that temperature
anisotropy allows A/IC waves and FM/W waves to become unstable at significantly
lower values of the alpha-particle beam speed $U_\alpha$ than in the
isotropic-temperature case. Likewise, differential flow lowers the minimum
temperature anisotropy needed to excite A/IC or FM/W waves relative to the case
in which $U_\alpha =0$. We discuss the relevance of our results to alpha
particles in the solar wind near 1 AU.
