The density matrix of the harmonic oscillator in thermostat is calculated by virtue of the coherent states method and coordinate-momentum intermediate representation. The density matrix of the harmonic oscillator in thermostat is presented only through choosing different parameter values without making use of Fourier-transformation relations and direct calculation. Furthermore, the direct way to calculate the density matrix is also shown and the corresponding result is closely related to Hermite polynomials. As a useful application of the above conclusions, a fully new relation on Hermite polynomials can be revealed by comparing both of the above equivalent results.