Do hot extension cords carry less current?

Yes, ambient temperature matters a lot. Extension cords have a rated ampacity based on a standard temperature (usually 30°C / 86°F). If it’s hotter, the cord can’t shed heat as well, so it must carry less current to avoid overheating and melting its insulation. For every 10°C above 30°C, derate by about 10% for common cords, so a 15-amp cord might only safely handle 12 amps in direct sun or a hot attic.