We have measured the long time (t = 5 to 200 h) heat release of Polymethylmethacrylate (PMMA) and Polystyrene (PS) at 70 mK less than or equal to T less than or equal to 300 mK. After cooling from om a ''charging'' temperature of 80 K the heat release in PMMA shows a t(-1) dependence in the measured rime and temperature ranges in agreement with the tunneling model. In contrast, for PS we observe strong deviations from a t(-1) dependence and a factor of ten smaller heat release than in PMMA in apparent contradiction to specific heat and thermal conductivity data for PS. To compare the heat release with other low temperature properties and to verify the consistency of the tunneling model we have measured also the acoustical properties (sound velocity and attentuation), the specific heat and the thermal conductivity of PMMA and PS in the temperature range 70 mK less than or equal to T less than or equal to 100 mK, 70 mK less than or equal to T less than or equal to 200 mK and 0.3 K less than or equal to T less than or equal to 4 K, respectively. We show that the anomalous time dependence of the heat release of PS is due to the thermally activated relaxation of energy states with excitation energies above 15 K.