Thermal　errors　adversely　affect　the　precision　of　a　machine　tool　operation.　Therefore,　reduction　of　thermal　errors　is　essential　for　improving　of　machining　accuracy.　In　this　paper,　in　order　to　realize　real-time　compensation,　taking　a　multi-axis　machine　tool　as　an　example　and　a　method　for　robust　modeling　and　predicting　thermally　induced　positional　error　is　proposed.　First　of　all,　the　number　of　temperature　measuring　points　required　in　thermal　error＇s　model　was　reduced　based　on　the　rough　set　theory,　which　greatly　reduced　variable　searching　and　modeling　time.　Then　through　grey　relation　theory,　systematic　analysis　of　the　similarity　degree　between　thermal　error　and　temperature　data　was　carried　out　to　select　sensitive　temperature　measuring　points,　and　the　temperature　variables　in　the　thermal　error＇s　model　were　reduced　from　24　to　7　after　optimization,　which　eliminated　the　coupling　problems.　For　reducing　the　influence　of　unpredictable　noises,　radial　basis　function　(RBF)　and　back　propagation　(BP)　neural　network　modeling　methods　were　adopted　to　predict　thermally　induced　positional　errors,　and　in　comparison,　the　prediction　accuracy　of　RBF　neural　network　was　found　superior　to　that　of　traditional　BP　neural　network.　Finally,　some　measured　data　were　selected　to　verify　the　validity　of　the　proposed　method,　and　the　results　showed　that　prediction　accuracy　of　the　proposed　thermally　induced　positional　error　model　was　reliable.