The present Letter puts forth a possible explanation for the outstanding problem of measured proton temperature anisotropy in the solar wind at 1 AU apparently being regulated by the mirror and oblique fire-hose instabilities. Making use of the fact that the local magnetic field intensity near 1 AU undergoes intermediate-scale temporal variations, the present Letter carries out the quasilinear analysis of the temperature anisotropy-driven instabilities with a time-varying local B field, assuming arbitrary initial temperature ratios and parallel betas. It is found that the saturated states in (β(∥), T(⊥)/T(∥)) space are bounded by the mirror and oblique fire-hose instabilities, which is superficially similar to the observation.