A mover stabilizing and stator cooling arrangement includes an upper sleeve surrounding the mover of the linear motor, a lower sleeve, a thermoconducting sleeve surrounding the stator and axially connected between the upper sleeve and the lower sleeve. The arrangement further includes a thermal grease filled in the space defined between the upper sleeve and the mover, the space defined between the thermoconducting sleeve and the stator, and the space defined between the lower sleeve and the outer tube for quick dissipation of waste heat. A stabilizer ring is set between the upper sleeve and the mover to stabilize axial movement of the mover. A piston and multiple one-way valve sets are mounted in the space between the lower sleeve and the outer tube for allowing adjustment of the volume in the thermoconducting sleeve responsive to expansion/contraction of the thermal grease due to temperature changes.