In transient experiments, it is common practice to employ thermochromatic liquid crystal (TLC) to measure the local heat transfer coefficients on the wall surface. This method depends on the solution of Fourier's conduction equation with the boundary conditions of the air temperature. It is impossible to create a step-change in the air temperature because of thermal inertia in the heater, or in the ducting upstream of the test section. Therefore, the local heat transfer coefficient must be calculated from a more general solution to the one-dimensional conduction equation. The present study describes a calibration method in the TLC, a design of a mesh heater, and a calculation procedure of the local heat transfer coefficient from the general solution to the one-dimensional conduction for a semi-infinite wall when the air temperature rises exponentially through the mesh heater. Also, an experiment is presented as an application of the present method to measure the local heat transfer distributions on the wall surface cooled by airflow and disturbed by vortex generators.