Cooling cap assembly and cooling unit

A cooling cap assembly comprising:

• a heat exchanger configured to be wrapped around a head of a patient;
• and
• a compression assembly separable from the heat exchanger, wherein the compression assembly comprises an enclosure and an inflatable member coupled to an internal surface of the enclosure, wherein the inflatable member comprises at least three chambers and when coupled, the inflatable member is positioned between the enclosure and the heat exchanger, wherein the heat exchanger is separate from and moveable relative to the inflatable member, wherein transitioning the inflatable member from a deflated configuration to an inflated configuration increases a contact area between the heat exchanger and to the head of the patient, and wherein the inflatable member comprises a top portion defining a longitudinal axis, a first side portion, a second side portion, and a base portion, and wherein the first and second side portions extend from the base portion at an acute angle with respect to the longitudinal axis.