TEBEG and TEEND control the temperature during an ab-initio mulecular dynamics. (see next section). If no initial velocities are supplied on the POSCAR file the velocities are set randomly according to a Maxwell-Boltzmann distribution at the initial temperature TEBEG. Velocities are only used for molecular dynamics (IBRION=0).
Mind that VASP defines the temperature as
But, because the center of mass is conserved there are only degrees of freedom (the sum of all velocities is zero, if a random initialization is chosen). This means that the real simulation temperature is
Also the temperature written by VASP (see e.g. OUTCAR file) is incorrect and has to be corrected accordingly. Usually the effect is rather small and subtle, but one should correct the error if very precise results are required. This means that a lower teperature should be specified according to
in the INCAR file.