Watch LookMovie. The 25th International 500-Mile Sweepstakes was held at the Indianapolis Motor Speedway on Monday, May 31, 1937. With temperatures topping out at 92 °F (33 °C), it is one of the hottest days on record for the Indy 500. To uproarious applause, Shaw, a 34-year-old Indianapolis resident, surged ahead in what remained the closest finish "500" until 1982: 2.16 seconds. Shaw finished the race with an average speed of 113.58 mph, and Hepburn was just behind him with an average speed of 113.565 mph.