Crosthwait was born on May 27, 1898 in Nashville, Tennessee. His father was a biology and chemistry teacher, and the principal of Nashville's first high school for African-Americans. The family moved to Kansas City, Missouri, where Crosthwait received his high school diploma in 1916. He went on to study at Purdue University where he earned both his B.S. and Master's degrees.

After receiving his Master's degree, Crosthwait became a consultant to engineering firms and public utilities, specializing in heating, cooling, and refrigeration technology. He designed and tested heating and ventilation systems, and introduced numerous electronic and mechanical inventions. Among his patents were an automobile turn signal, a component for thermostats, a vacuum pump, and several other devices related to heating systems. Crosthwait also designed a steam system that was used to heat the towers of Radio City in New York, New York.