The heater would need replacing, possibly also the thermal fuse if you can use a multimeter and have the knowledge it is possible to do yourself.
If you require a repair service we offer this for £19.50 with 3 month warranty at www.siriushair.com
siriushair
February 2015
you can buy the kit to fix it from e bay.comes with two elements,the thermal fuse.all you need to repair it,cost is around £14.00 look it up on e bay
gts
January 2015
if the heating element is gone in one side, all you can do is replace the unit for a new one, cost more to get it fixed,,
howtomendit.com for free repair help, information and advice.
Try fixfault.com to fix hair straighteners.