A temporal surge was a brief but intense rise in temporal energy.
In 2371, a temporal surge caused by an exploding microscopic singularity passing through the Sol system shifted the chronitons lodged in the ablative armor matrix of the USS Defiant into a high state of temporal polarization. This caused a transporter beam passing through the polarized particles carrying Captain Benjamin Sisko, Lieutenant Jadzia Dax, and Doctor Julian Bashir, to be redirected through time, causing them to materialize in San Francisco, the year 2024. (DS9: "Past Tense, Part I")
In 2372, when Quark, Rom, Nog, and Odo accidentally traveled to the year 1947 through a time warp, Rom was able to harness the beta radiation from a nuclear explosion to trigger a cascade reaction in the kemacite being stored in their shuttle. This had the effect of causing a temporal surge in the subspace continuum, recreating the time warp and returning them to their own time. (DS9: "Little Green Men")