Thermal　deformation　is　the　main　factor　of　the　machining　accuracy　for　grinding　machines,　which　seriously　restricts　the　precision　improvement　of　grinding　machines.　However,　at　present,　there　are　little　researches　on　thermal　error　prediction,　and　the　accuracy　of　the　prediction　model　is　comparatively　low.　Thus,　a　novel　approach　for　thermal　deformation　prediction　of　grinding　machine　spindle　based　on　heat　energy　conduction　principle　and　neural　network　is　proposed　in　this　paper.　Firstly,　the　temperature　sensors＇　pairs　are　applied　to　measure　the　temperature　deviation　between　the　spindle　surface　and　its　adjacent　ambient　which　are　directly　related　to　the　heat　energy　exchange.　Secondly,　the　temperature　deviations　of　each　segment　of　the　spindle　are　taken　as　inputs,　which　will　exist　and　accumulate　in　the　form　of　heat　energy　subsequently　in　the　convolutional　neural　network.　Meanwhile,　the　accumulated　heat　energy　is　mixed　and　transferred　to　the　different　segments　of　the　spindle　in　the　convolutional　neural　network.　Thirdly,　the　thermal　deformation　caused　by　the　increment　of　heat　energy　is　considered　as　the　output　of　thermal　error　prediction　result　based　on　the　principle　of　heat　energy　conduction.　Finally,　the　simulations　and　experiments　are　implemented　to　validate　the　feasibility　and　effectiveness　of　the　proposed　method.