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We have developed a new method to measure the viscosity of micrometric films by thermomechanical analysis with a hemispherical probe of millimetric diameter. The loading curve (displacement vs. time) recorded as the probe tip crosses the whole film at constant load until it touches the substrate is fitted to a theoretical curve shape that has been obtained after solving the problem of liquid flow under the probe tip. The method has been validated by measuring the viscosity of rosin films. It has been applied to analyze the thermal evolution of unstable liquid films that appear on Ba propionate, Ce(III) propionate and a low-fluorine precursor film of YBa2Cu3O6+x. During pyrolysis of the last two films, viscosity first diminishes due to heating and then it increases as solid oxide particles are formed inside the liquid.