It comes after an investigation found a third of UK retailers and manufacturers are selling straighteners without safety devices, such as heat-proof pouches.
Burns specialists at Yorkhill Children's Hospital said they were "concerned" about the number of injuries they were seeing caused by the devices.
Figures show around around 27 children a year -more than two each month - are taken the hospital's emergency department with burns caused by straighteners.
The report also found three quarters of parents did not use pouches to store their straighteners and a quarter admitted leaving them to cool down on the floor.
Straighteners can reach temperatures of 235C and stay hot up to 15 minutes after being switched off.
Nearly a third of adults in Glasgow said they had received a burn from a heated hair appliance.
Sharon Ramsay, Burns Nurse Specialist at Yorkhill said: "Contact burns can cause permanent scarring and be very painful. We urge everyone to be careful when using these devices."
Emma Apter, from the Electrical Safety Council, said: "It's really worrying that retailers and manufacturers are selling products that can reach 235C without explaining the dangers."