We propose a new quantum simulation method for a many body quantum liquid of identical particlesat finite (non-zero) temperature. The new scheme expands the high temperature density matrix on the over complete set of single particles coherent states of John Rider Klauder instead of the usual plane waves as in conventional path integral methods. One is free to tune the elastic constant and/or the mass of the harmonic oscillator subtending the coherent states so as to maximize the computational efficiency of the algorithm. We prove that in the limit of an extremely stiff harmonic oscillator the results for the internal energy tends towards the correct expected values. Moreover we suggest that a stiff harmonic oscillator could allow the use of larger (imaginary) timesteps. This additional degree of freedom is the characteristic feature of our new algorithm and is not available in more conventional path integral methods.