The　main　processing　unit　of　Wire　cut　Electrical　Discharge　Machining-Low　Speed　is　up　and　down　wire　rack.　The　wire　rack　is　a　cantilever　structure.　Axial　error　is　greatly　affected　by　the　ambient　temperature　and　reflects　on　the　workpiece　directly,　seriously　affecting　the　machining　accuracy.　In　this　paper,　respectively　using　theoretical　calculations　and　finite　element　methods　to　analyze　the　impact　of　changes　in　ambient　temperature　on　the　deformation　of　the　upper　and　lower　wire　rack,　and　in-depth　analysis　of　its　thermal　error,　to　get　the　thermal　deformation　characteristics　of　the　WEDM-LS＇　up　and　down　wire　rack.