Do higher rated SSRs produce less heat
Most Solid State Relays use either a triac or inverse-paralell-connected SCRs as the switch element.

The forward voltage drop when the switch is turned ON is about 1 Volt (average). This voltage drop is relatively constant, no matter what the current rating of the switch element is. 

So, no. I don't think that using a SSR that is much larger than is actually needed will give significantly lower losses.