The relationship of time-resolved surface heat flux to the turbulent free-stream flow over a turbine blade is investigated. Measurements are made in a transonic linear cascade with a modem high pressure turbine blade profile. Time-resolved direct heat transfer measurements are made with Heat Flux Microsensor (HFM) inserts along the pressure side, and with one HFM directly deposited on the suction surface near the leading edge. Simultaneous velocity measurements are made above the heat flux sensors using miniature hot-wire probes. Grids are used to produce two turbulence fields of constant inlet turbulence intensity, Tu = 5%, but significantly different integral length scales (Ax). Results are compared with a low free-stream turbulence baseline condition. Special emphasis is given to frequency domain analysis of the data via coherence function magnitude and phase, energy spectra, and time auto- arid cross-correlations. Results are presented for both mean and fluctuating velocity and heat flux. Mean heat transfer is highest for the smaller length scale grid, but inlet integral length scale appears of limited use in predicting surface heat flux interactions with the observed complex passage flow. While free-stream rms velocity, u', and surface rms heat flux, q', show some correlation with mean heat transfer in the laminar region near the leading edge, no such correlation is seen on the pressure side. Instead, u' decreases along the pressure side while low frequency transitional activity causes q' to increase. Application of laminar heat transfer correlations to the near leading edge region shows some success. However, application of laminar and turbulent heat transfer correlations along the pressure side gives poor results which are likely due to the transitional state of the boundary layer and complex flow. Frequency domain analysis allowed estimation of scales, frequency, and time lag across the boundary layer of passing flow structures. Coherence between free-stream velocity and surface heat flux was found useful for determining the scale and frequency range of free-stream turbulent structures interacting with the surface heat flux, but did not correlate with mean heat transfer. Suction side coherence was low relative to the pressure side and isolated to a narrow frequency band. Pressure side coherence was broadband with significant low frequency energy near the leading edge. This low frequency energy (larger structures) decayed along the pressure side while higher frequency coherent structures were seen to grow. / Ph. D.