Yes, cold for sure, -78 is standard conditions for this reaction.
The chemistry comes from a paper for the synthsis of a pheromone. They make the trisubstituted epoxide last, even though as you can see from the product above, it would be a diolefin. In theory the trisubstituted olefin will react "first/faster" than the disubstituted olefin would. But in practice that is not true. Using 1 eq mCPBA in DCM at 0 deg C, both the monoepoxide (product above) and the diepoxide were made with the starting diene also left after the oxidation. I think it is a concentration phenomena.
So we are trying to epoxidize first, then carry through to the last reaction of alkylating with methyllithium. It wont give us the un-wanted diepoxide.