Consider - if you are talking about Renaissance with steam engines, this indicates not the death of Hephaestus, but something more like his rise to power.
Moreover, if you look at some of the Greek dramas, especially Aeschylus, you find that the seed of Zeus' destruction is given to Prometheus, by Themis*. There is a marriage that will produce offspring that will bring down Zeus, and Prometheus knows who it is.
And an alliance between Hephaestus and Prometheus seems natural - Prometheus would like to pass some of Heph's secrets on to man, and Heph wants to earn a little gosh-darned respect around here!
Tie that into the usual godly struggles, and it sure looks like a source of a Renaissance, to me. Due to a prophecy of Themis, Heph, Prometheus, and Athena form a bit of a power block, and an "Age of Reason" begins? What's more appropriate than that?
*Who is in the play more like Gaia. So his mother or his aunt, depending on how you read it - as his aunt, she's another titan, who's purview was natural law and custom, and has the gift of prophecy.