In a scroll fluid machine, a fixed scroll has a fixed wrap, and an orbiting scroll has an orbiting wrap which engages with the fixed wrap to form a compressing chamber between the orbiting and fixed wraps. The orbiting scroll is rotatably mounted around an eccentric axial portion of a driving shaft and revolved by the driving shaft. A gas introduced from the outer circumference of the fixed scroll is compressed in the compressing chamber as it flows towards the center. Parts near the center is heated by a compressed gas. On the other surface of the fixed scroll to the surface having the fixed wrap, a plurality of cooling fins are provided. Air is introduced between the cooling fins to cool the machine. Between the cooling fins, a heat-releasing projection is provided to improve cooling efficiency.