The hundreds of multiple planetary systems discovered by the Kepler mission are typically observed to reside in close-in (≲ 0.5 AU), low-eccentricity, low-inclination orbits. We run N-body experiments to study the effect that unstable outer (≳ 1 AU) giant planets, whose end orbital configurations resemble those in the Radial Velocity population, have on these close-in multiple super-Earth systems. Our experiments show that the giant planets greatly reduce the multiplicity of the inner super-Earths, and the surviving population can have large eccentricities (e≳ 0.3) and inclinations (I≳ 20^\circ ) at levels that anti-correlate with multiplicity. Consequently, this model predicts the existence of a population of dynamically hot single-transiting planets with typical eccentricities and inclinations of ∼0.1-0.5 and ∼10°-40°. We show that these results can explain the following observations: (I) the recent eccentricity measurements of Kepler super-Earths from transit durations; (II) the tentative observation that single-transiting systems have a wider distribution of stellar obliquity angles compared to the multiple-transiting systems; (III) the architecture of some eccentric super-Earths discovered by Radial Velocity surveys such as HD 125612c. Future observations from TESS will reveal many more dynamically hot single transiting planets, for which follow up radial velocity studies will be able to test our models and see whether they have outer giant planets.