When I had candle wax to remove last month, I did a search and read on a previous post here on CIU about using a hairdryer and vacuum method.
This was really successful for the red wax I had to remove, but the stain left behind from the red dye was more difficult to deal with. Some success with red RX iron and damp towel.
With the hairdryer hold slightly away from the wax and be careful not to overheat the carpet as the fibres could be damaged. At the same time using the nozzle on the vacuum to suck up the wax as it slowly becomes pliable. Like magic the wax will be sucked up into the vacuum. However, there will be small residue of wax coating the inside of the vacuum tube but this is minimal and won't affect the equipment.
Good luck with it, but make sure your customer knows that you may not be able to remove 100% of the wax dye.
Regards,
Ben