Upcoming direct-imaging experiments may detect a new class of long-period, highly luminous, tidally powered extrasolar gas giants. Even though they are hosted by ~ Gyr-old main-sequence stars, they can be as hot as young Jupiters at ~100 Myr, the prime targets of direct-imaging surveys. They are on years-long orbits and presently migrating to feed the hot Jupiters. They are expected from high-e migration mechanisms, in which Jupiters are excited to highly eccentric orbits and then shrink semi-major axis by a factor of ~10-100 due to tidal dissipation at close periastron passages. The dissipated orbital energy is converted to heat, and if it is deposited deep enough into the atmosphere, the planet likely radiates steadily at luminosity L ~ 100-1000 L_Jup(2 x 10-7-2 x 10-6 L_Sun) during a typical ~ Gyr migration timescale. Their large orbital separations and expected high planet-to-star flux ratios in IR make them potentially accessible to high-contrast imaging instruments on 10 m class telescopes. ~10 such planets are expected to exist around FGK dwarfs within ~50 pc. Long-period radial velocity planets are viable candidates, and the highly eccentric planet HD 20782b at maximum angular separation ~0.08 is a promising candidate. Directly imaging these tidally powered Jupiters would enable a direct test of high-e migration mechanisms. Once detected, the luminosity would provide a direct measurement of the migration rate, and together with mass (and possibly radius) estimate, they would serve as a laboratory to study planetary spectral formation and tidal physics.