A suspended system for measuring the thermal properties of membranes is presented. The sensitive thermal measurement is based on the 3ω dynamic method coupled to a Völklein geometry. The device obtained using micro-machining processes allows the measurement of the in-plane thermal conductivity of a membrane with a sensitivity of less than 10 nW/K (+∕-5 × 10(-3) Wm(-1) K(-1) at room temperature) and a very high resolution (ΔK/K = 10(-3)). A transducer (heater/thermometer) centered on the membrane is used to create an oscillation of the heat flux and to measure the temperature oscillation at the third harmonic using a Wheatstone bridge set-up. Power as low as 0.1 nW has been measured at room temperature. The method has been applied to measure thermal properties of low stress silicon nitride and polycrystalline diamond membranes with thickness ranging from 100 nm to 400 nm. The thermal conductivity measured on the polycrystalline diamond membrane support a significant grain size effect on the thermal transport.