The invention relates to a micro heat exchanger device and method using non-stationary oscillatory effects. The inventive method consists in passing a working fluid through a first microchannel which opens into a second microchannel having a larger cross-section owing to a sudden expansion (typically in the form of a step). Both the flow rate and the pressure gradient at the inlet of the first microchannel are oscillated in a pre-determined manner. The oscillation of the dynamic fluid variables at the inlet of the first microchannel produces a non-stationary effect in the fluid field, which in turn changes the local topology of the flow in the second microchannel. The aforementioned local changes, which are amplified by the sudden expansion between the two microchannels, generate an increase in the transfer of heat between the working fluid and the walls of the second microchannel.