I believe no. This is yet another urban legend, spreading via mails and social networks. I decided to blog about it after seeing too many posts like – “A 21 year old guy had worn a pair of contact lenses during a barbecue party. After a few minutes, he started to scream for help and moved rapidly, jumping up and down….”.
A quick googling shows that contact lenses’ melting points are about 90°C. Some sites suggest that contact lenses can be boiled to disinfect them. Do you think your eyes and face can stand that much heat?
The bottom line is, before the contact lenses melt on your eyes, your face’s skin might have burnt out.
Something which people disregard is not wearing the contact lenses for too long. If you wear them for too long then the portion between your eyes and the lenses might dry up while rest of the eyes are wet. This could result in suction force that may prevent the lenses from being removed.
Disclaimer: I don’t wear contacts and have no experience about them. All the above information have been collected over net.