Multiple penetration heat flow surveys that employ ''violin bow'' multithermistor array instruments generate large quantities of high-quality data. To cope with the problems associated with the reduction of these data, an algorithm has been developed which can be used to reduce the data automatically on a microcomputer. The algorithm is designed for use with a pulsed line source method. The multiply iterative algorithm deals, on a sensor by sensor basis, with errors associated with nonideal probe construction and sediment entry, factors that affect the determination of both in situ temperatures and themal conductivities. Numerical tests of the algorithm show that it is accurate and stable and fast enought for post-real-time reduction of data at sea. Practical tests on high-quality data from the western Pacific show that accuracies are limited by the instrumental resolution; in these cases, the reduction algorithm provided determinations of undisturbed in situ temperatures to better than 1 mK and of in situ conductivities to within 1%. ¿ American Geophysical Union 1987