This paper describes the development of an experimental arrangement and the application of acetone-based planar laser-induced fluorescence (PLIF) measurement techniques to study the unsteady characteristics of heat transfer processes in the parallel-plate heat exchangers of thermoacoustic devices. The experimental rig is a quarter-wavelength acoustic resonator where a standing wave imposes oscillatory flow conditions. Two mock-up heat exchangers, 'hot' and 'cold', have their fins kept at constant temperatures by electrical heating and water cooling, respectively. A purpose-designed acetone tracer seeding mechanism is used for PLIF temperature measurement. Acetone concentration is optimized from the viewpoint of PLIF signal intensity. Two-dimensional temperature distributions in the gas surrounding the heat exchanger plates, as a function of phase angle in the acoustic cycle, are obtained. Local and global (instantaneous and cycle-averaged) heat flux values on the fin surface are estimated and used to obtain the dependence of the space-cycle averaged Nusselt versus Reynolds number. Measurement uncertainties are discussed.