To alleviate pressure on someone. Take the heat off of her—you know she'll pay up eventually.
take the heat off (of)someone or something
Fig. to relieve the pressure on someone or something. (Of is usually retained before pronouns.) That really takes the heat off of all of us. The change in the deadline takes the heat off the office staff.
take the heat off someone
tv. to relieve the pressure on someone; to free someone from suspicion, responsibility, a deadline, etc. The confession by Rocko took the heat off the cop-shop for a while.