A profile map of parameter values in a region is determined based on average values along linear paths through the region. In one example, a temperature map of a region of a gas turbine engine is created based on time-of-flight measurements from acoustic transceiver pairs arranged circumferentially around the region. A speed of sound for each transceiver pair is determined based on the time-of-flight measurements. An average temperature along each path is estimated from the time of flight, and the profile map is computed from the average temperatures. The profile map may be computed using a polynomial approximation technique, a grid optimization technique or a basis function technique.