Excitation of electromagnetic waves propagating across a beam of charged plasma particles has been investigated and thermal motion taken into account. The excitation of electromagnetic waves is shown to occur both at directed beam velocities exceeding thermal particle velocities and at velocities smaller than the thermal velocities of plasma particles. With a slow beam whose directed velocity is smaller than any kind of thermal particle velocity in the system, excitation of electromagnetic waves does not occur. With an external magnetic field, excitation of waves propagating across a magnetic field (and consequently, across a beam) occurs at u2 > νA12 + νA22, where νA1 and νA2 are the Alfvén velocities, in the beam and in the quiescent plasma respectively.