An electro-mechanical setup for the measurement of AC-forces in a low-temperature tunnelling microscope has been developed, which enables extremely high force resolution. The crosstalk of vibrations onto the tunnelling current is used to measure the deflection of a force-sensing cantilever beam. We demonstrate its capability to measure the noise of the force at a tunnelling contact using polycrystalline Iridium. Depending on temperature, spring constant and current, a resolution in the range of $\rm {fN}/\sqrt{\rm Hz}$ is possible. We observe peak levels of the force-noise at the energy of the expected phonon maximal density of states, which suggests that inelastic transport processes contribute to force fluctuations.An electro-mechanical setup for the measurement of force-noise properties in a low-temperature tunnelingmicroscope has been utilized to enable extremely high resolution and acquire force-noise spectra as function of the applied voltage bias. The direct crosstalk of vibrations onto the tunneling current is used to measure the deflection of a force-sensing cantilever. We demonstrate its capability to measure the mechanical energy of the cantilever, caused by the noise of the force from vacuum tunneling between polycrystalline Iridium electrodes. We observe peak levels of the induced cantilever energy at polarity-symmetric voltages corresponding to dominant peaks of the phonon density of states, which suggests that inelastic transport processes contribute to force fluctuations.