A combination of broadband dielectric (10(-2) Hz-10(9) Hz) and specific heat (10(-3) Hz-2x10(3) Hz) spectroscopy is employed to study the molecular dynamics of the glass-forming nematic liquid crystal E7 in a wide temperature range. In the region of the nematic phase the dielectric spectra show two relaxation processes which are expected theoretically: The delta relaxation which corresponds to rotational fluctuations of the molecules around its short axis and the tumbling mode at higher frequencies than the former one. For both processes the temperature dependence of the relaxation rates follows the Vogel-Fulcher-Tammann formula which is characteristic for glassy dynamics. By applying a detailed data analysis, it is shown that close to the glass transition the tumbling mode has a much steeper temperature dependence than the delta process. The former has a Vogel temperature which is by 30 K higher than that of the delta relaxation. Specific heat spectroscopy gives one relaxation process in its temperature and frequency dependence which has to be assigned to the alpha relaxation (dynamic glass transition). The unique and detailed comparison of the temperature dependence of the dielectric and the thermal relaxation rates delivers unambiguously that the dielectric tumbling mode has to be related to the dynamic glass transition.