Four plasma instabilities driven by proton temperature anisotropies are investigated theoretically by using Whang's ion model, i.e., heat flux modified non-Maxwellian velocity distribution functions. The linear dispersion properties are studied in an infinite Vlasov plasma where the proton distribution is assumed to consist of one warm slow-speed component and the electron background is isotropic. The parameters are chosen according to Whang's solar wind ion model. It is shown that the fire hose. mirror, and Harris instability do not occur under these conditions. The only unstable mode is the ion cyclotron mode. Growth rates are found to have values between 2.1 ⋅ 10-2 (T∥/T⊥ = 2) and 1.1 ⋅ 10-4 (T⊥/T∥ = 0.15).