"Building a fire under" is an expression used to describe the act of motivating or pressuring someone in order to get them to act. Antonyms for this phrase would center around words that imply calmness and relaxation, rather than urgency and pressure. Some possible antonyms for "building a fire under" might include words like soothing, calming, relaxing, tranquilizing, or pacifying. These words suggest a much more gentle and laid-back approach to getting someone to do something, as opposed to the more aggressive and forceful approach implied by "building a fire under." Depending on the context, any of these antonyms could be used to describe a more peaceful, less hurried way of motivating others.