Thermal　issues　are　becoming　increasingly　critical　due　to　rising　power　densities　in　high-performance　chip　design.　The　need　for　fast　and　precise　full-chip　thermal　analysis　is　evident.　Although　machine　learning　(ML)-based　methods　have　been　widely　used　in　thermal　simulation,　their　training　time　remains　a　challenge.　In　this　article,　we　proposed　a　novel　physics-informed　separation　of　variables　solver　(PISOV)　to　significantly　reduce　training　time　for　fast　full-chip　thermal　analysis.　Inspired　by　the　recently　proposed　ThermPINN,　we　employ　a　least-square　regression　method　to　calculate　the　unknown　coefficients　of　the　cosine　series.　The　proposed　PISOV　method　combines　physics-informed　neural　network　(PINN)　and　separation　of　variables　(SOVs)　methods.　Due　to　the　matrix-solving　method　of　PISOV,　its　speed　is　much　faster　than　that　of　ThermPINN.　On　top　of　PISOV,　we　parameterize　effective　convection　coefficients　and　power　values　for　surrogate　model-based　uncertainty　quantification　(UQ)　analysis　by　using　neural　networks,　a　task　that　cannot　be　accomplished　by　the　SOV　method.　In　the　parameterized　PISOV,　we　only　need　to　calculate　once　to　obtain　all　parameterized　results　of　the　hyperdimensional　partial　differential　equations.　Additionally,　we　study　the　impact　of　sampling　methods　(such　as　grid,　uniform,　Sobol,　Latin　hypercube　sampling　(LHS),　Halton,　and　Hammersly)　and　hybrid　sampling　methods　on　the　accuracy　of　PISOV　and　parameterized　PISOV.　Numerical　results　show　that　PISOV　can　achieve　a　speedup　of　245x　,　and　10(4)x　over　ThermPINN,　and　PINN,　respectively.　Among　different　sampling　methods,　the　Hammersley　sampling　method　yields　the　best　accuracy.