The molecular dynamics of the discotic liquid crystal pyrene-1,3,6,8-tetracarboxylic tetra(2-ethylhexyl)ester is studied by dielectric relaxation and specific heat spectroscopy. Dielectric spectroscopy shows 3 processes: a β-relaxation at low temperatures and an α-relaxation in the temperature range of the mesophases followed by conductivity. The dielectric α-relaxation is assigned to a restricted glassy dynamics in the plastic crystal as well as in the liquid crystalline phase. The obtained different Vogel-Fulcher-Tammann laws (different Vogel temperatures and fragility) are related to the different restrictions of the dipolar fluctuations in the corresponding phases. By means of specific heat spectroscopy glassy dynamics is also detected in the plastic crystalline phase but with quite a different temperature dependence of the relaxation times. This is discussed considering the different probes involved and how they are influenced by the structure. In the frame of the fluctuation approach a correlation length of glassy dynamics is calculated to 0.78 nm which corresponds to the core-core distance estimated by X-ray scattering.