A new instrument to continuously determine the remanent magnetisation of standard paleomagnetic (inch-sized) rock samples during heating and cooling (continuous thermal demagnetisation) was developed. The design as an off-axis spinner magnetometer (i.e. the samples rotate on a circular path in a radial distance to the spinning axis) allows the simultaneous measurement of several samples and offers a way to determine the full vector of magnetisation. Six fluxgate sensors are used to record three gradients of the magnetic fields caused by the samples and the vector of remanence is determined by regression analysis of the gradient signals. The sensitivity of the instrument is 2.10 (super -7) Am (super 2) . Hot air is circulating through copper pipes which heat the samples by thermal radiation to avoid magnetic fields which would arise from direct electrical heating. Currently, the measurements are restricted to a maximum of 350 degrees C. The instrument was tested with oceanic basalt samples that were given an artificial remanence. Some continuous thermal demagnetisation experiments of this artificial remanence and of the natural remanent magnetisations are shown for oceanic basalts.