This thesis is composed by three projects in which we investigate thermal effects in low dimensional quantum spin systems. Thanks to recent developments in DMRG/MPS techniques, it is possible to simulate for such systems the dynamics at finite temperature. This allows us in the first two parts to study the temperature dependence of the NMR spin-lattice relaxation rate and of the INS spectra. Numerical calculations are performed for a wide range of temperatures. This represents a bridge between analytical results available for very low and very high temperatures. Interesting deviations from bosonization results valid at low energy, are seen at temperatures comparable to the energy scale of the system. In the third part we study the temperature and magnetic field dependence of the Grüneisen parameter, a valuable quantity for the detection and investigation of quantum phase transitions. Using an effective theory valid close to criticality, we show deviations from the critical behavior.