A description is given of some measurements made on a north-south section across the Cayman Trench using a precise bathythermograph with quartz crystal temperature sensors. The main instrument specifications are given. The observations revealed that the water above 4300 m was stably stratified. Below this depth the temperature gradient was within 2% of the adiabatic temperature gradient and the water stability was presumed to be positive almost everywhere but very small. Salinities were nearly uniform below 2500 m. Also, below 4300 m the observed temperatures at the deep stations for a given depth, were bracketed in a range of less than 0·003°C. This corresponds to isotherm slopes of the order of 2 × 10-4 °C km-1. Irregularities in the potential temperature-depth curves with scales of about 1 × 10-3 °C and 100 m respectively were observed. For length scales of the order of 2 m, temperature variations are inferred to be less than the limit of resolution, which was about 2 × 10-4 °C. The assumption that geothermal flux is currently being trapped in the water below 4300 m, combined with the history of temperature increases enables, an estimate to be made of the mean geothermal flux value. A value of 2·3 μ cal cm-2 sec-1 is estimated. © 1969.