Solid State Relay Heat Release
AD-SSR6T25-DC-280A is a triac based SSR, as such you can expect a 2V drop, so at 400mA expect it to make about 800mW of heat plus whatever power it takes in the input.
At about 1W it should be fine inside a metal enclosure. (that's about 3.4btu/hr in American units)
The brief inrush current will be happening to a cold relay, and as such it can be ignored.