An underactuated nonholonomic robot with a bounded control input travels with a constant speed in a 3D workspace. An unknown time variant scalar field is defined on this workspace. The robot should detect, locate, and densely sweep a moving and deforming 2D isosurface (level set), which is the locus of points where the field takes a given value. The sensory data consist of the value of the field at the current location, robot's coordinate along a certain (typically, vertical) space direction, and the orientation of this direction relative to the robot. We offer a new navigation law under which the robot reaches the targeted isosurface from an occasional initial location and then scans the part of this surface in between two given 'altitudes'. This law does not rely on estimation of the field gradient and is undemanding in terms of motion and computation. Its convergence is demonstrated by a mathematically rigorous result and computer simulation tests.