We studied the temperature dependence of heat capacity C-P(T) of a quasi-one-dimensional magnetic system beta-TeVO4, in a zero magnetic field and a temperature region of 0.1 K <= T <= 300 K. The C-P(T) dependence shows phase transitions at temperatures of 4.65, 3.28, and 2.32 K. Is it established that at a temperature of T-N = 4.65 K there is a phase transition from a paramagnetic to an antiferromagnetic state. We provide a theoretical description of the heat capacity's temperature dependence. (C) 2015 AIP Publishing LLC.