In short, no. Contact lenses will not melt in common heat. Contact lenses are sterilized at temperatures of up to 250 degrees Fahrenheit, and dirty contact lenses that need to be cleaned or re-sterilized are often placed in boiling water.
If contact lenses can withstand boiling water without being destroyed, a heat source would have to be hot enough to boil away the tears in your eyes before your lenses would even begin to sustain damage. Needless to say, this level of heat is not reached by any common source you would encounter day to day.