Internal dissipation in a tidally perturbed librating body differs in several respects from the tidal dissipation in a steadily spinning rotator. First, libration changes the spectral distribution of tidal damping across the tidal modes, as compared to the case of steady spin. This changes both the tidal heating rate and the tidal torque. Second, while a non-librating rotator experiences alternating deformation only due to the potential force exerted on it by the perturber, a librating body is also subject to a toroidal force proportional to the angular acceleration. Third, while the centrifugal force in a steadily spinning body renders only a permanent deformation (which defines the oblateness when the body cools down), in a librating body this force contains two alternating components-one purely radial, another a degree-2 potential force. Both contribute to heating, as well as to the tidal torque and potential (and, thereby, to the orbital evolution).We develop a formalism needed to describe dissipation in a homogeneous terrestrial body performing small-amplitude libration in longitude. This formalism incorporates as its part a linear rheological law defining the response of the rotator's material to forcing. While the developed formalism can work with an arbitrary linear rheology, we consider a simple example of a Maxwell material. We demonstrate that, independent of the rheology, forced libration in longitude can provide a considerable and even leading-and sometimes overwhelming-input in the tidal heating. Based on the observed parameters, this input amounts to 52% in Phobos, 33% in Mimas, 23% in Enceladus, and 96% in Epimetheus. This supports the hypothesis by Makarov and Efroimsky (2014) that the additional tidal damping due to forced libration may have participated in the early heating up of some of the large moons. As one possibility, such a moon could have been chipped by collisions-whereby it acquired a higher permanent triaxiality and, therefore, a higher forced-libration magnitude and, consequently, a higher heating rate. After the moon warms up, its permanent triaxiality decreases, and so does the tidal heating rate.