Abstract. Combined vertical current (w) and thermistor string data demonstrate that high-, near-buoyancy frequency internal "wave" trains along a pycnocline in a flat-bottom shelf sea consist for 2 periods of a dominant mode-1 non-linear part, while thereafter mainly of linear [mode-2, quadrupled frequency] waves, to first order. In a simple [linear] heat budget the use of unfiltered temperature gradient or its time mean changes results by only 10%. The observations also demonstrate that temperature is not always adequate to estimate vertical motions using the linear 1-D heat equation. In shallow seas, tidal-w estimated from temperature data can be an order of magnitude weaker than directly observed w, and thus do not represent free internal waves. In the ocean, not too far from the main internal wave topography source, tidal motions represent linear waves and are well described by temperature-inferred w. There however, temperature-inferred w and directly observed w differ strongly near the buoyancy frequency, at which w is dominated by non-linear waves, and near [sub]inertial frequencies, at which w is dominated by eddies and gyroscopic waves.