This　paper　proposes　a　novel　fast　analytical　method　for　full　chip　thermal　analysis　with　reduction　from　3D　to　2D　by　using　the　effective　thermal　characteristic　length,　called　Stepwise　Integration　Separation　of　Variables　(SISOV).　Unlike　the　traditional　Separation　of　Variables　(SOV)　method,　which　relies　heavily　on　numerical　approximation　integration　for　Fourier　series　coefficient　calculation,　the　proposed　SISOV　employs　analytical　stepwise　integration　by　leveraging　the　uniform　power　densities　across　each　block.　This　analytical　technique　mitigates　discretization　errors　typically　encountered　in　numerical　integration,　enhancing　the　accuracy.　To　overcome　the　inefficiencies　inherent　in　the　plain　SOV　method,　we　propose　an　adaptive　rectangular　mesh　strategy　to　discretize　the　chip.　This　approach　markedly　reduces　the　number　of　required　meshed　blocks　compared　to　grid　sampling　points,　leading　to　a　more　efficient　calculation　of　coefficients.　Finally,　the　fast　SISOV　method　is　applied　in　the　thermal　uncertainty　quantification　(UQ)　analysis　of　the　full　chip.　The　numerical　results　show　that　the　proposed　SISOV　outperforms　the　plain　SOV　method,　providing　a　speedup　ranging　from　2　to　63　times.　Moreover,　its　accuracy　surpasses　that　of　the　SOV　method,　with　a　Mean　Absolute　Error　(MAE)　of　just　0.05　K,　indicating　a　substantial　improvement.　The　thermal　conductivity　UQ　analysis　reveals　that　the　SISOV　method　and　the　plain　SOV　method　can　achieve　26×　and　9×　faster　performance　compared　to　COMSOL,　respectively.　IEEE