In 2012, four MIT alums set out to give menswear the comfort and performance of gym clothes. They named their company Ministry of Supply after a World War II-era division of British intelligence that employed the real-life inspiration for James Bond’s gadget-happy sidekick, Q. The company has created machine-washable suits and 3-D-printed sweaters.

Next month, Ministry of Supply will release the Mercury, which it describes as “the first intelligent heated jacket” for men and women. Lightweight carbon-fiber heating elements...