Those on foot don't last long in the heat. Essentially, all is heat-locked. People will seek a cool spot and wait for whatever comes. On the other side of the Earth perpetual night is reigning. Businesses do not open as everyone is confused.
Telephone lines are also jammed, and lack of coordination is evident everywhere.
The night shift goes home, eventually, exhausted, but the day shift never shows up. The traveler attempting to drive somewhere finds gas stations unattended and cars out of gas blocking the roads. So those becoming aware of the situation at the last minute do not go anywhere, essentially, whether they want to or not. The exception might be the wealthy or powerful who have maintained a plane, fueled and ready, and find all these arrangements working well when the crisis arrives. Private landing strips and well-stocked country estates make a last minute flight to safety possible.