if the heatsink is outside the box, you might be ok. the closer to full capacity you run the SSRs, the more they heat up. so if you were only switching 5 amps with 40 amp SSRs, they wouldnt heat up much at all. but if you were switching close to 40 amps on each of them, you are going to have a lot of heat.
SSRs can generate quite a bit of heat,and when they get to hot can stick open or closed.
i wouldnt describe it that way, atleast not in the sense that they will unstick when cooled again, or the way a mechanical relay could overheat. when you heat any semiconductor past its safe operating temp, you fry it. the circuitry turns into charcoal, and an overheated SSR could either fail open and block all voltage, fail closed and perminantly conduct power, or a mixture of the two. it depends on what part(s) exactly got fried.