This paper describes a new method to determine the heat transfer coefficient, h, and the adiabatic-surface temperature, T-ad, from transient measurements of the surface temperature of a test piece. Maximum Likelihood Estimation (MLE) is used in conjunction with Fourier's 10 equation to determine the optimum values of h and T-ad, and also their 95% confidence intervals, without having to measure the air temperature. Validation experiments are conducted in a small purpose-built wind tunnel, and a novel infra-red (IR) sensor is used to measure the surface temperature of the test piece. A mesh heater is used to generate either a step-change in the air temperature or a 'slow-transient' in which the air temperature - and consequently T-ad - increases slowly with time. Numerical simulations, using 'noisy data', show that the computations give accurate estimates of h and T-ad for both the step-change and slow-transient cases. The values of h and T-ad determined from the measurements in the wind-tunnel are in good agreement with empirical correlations for turbulent flow over a flat plate. An advantage of the new method is that it can be used for all transient experiments, even those slow transients that violate the assumption of a semi-infinite solid, an assumption that is used in most existing analysis methods. The new method, which was applied here to boundary-layer flow with one stream of fluid, could also be applied to 'three-temperature problems', like film cooling, which involve two streams of fluid. The significant advantage of using the method for these problems is that both h and T-ad could be determined accurately from a single experiment. (C) 2016 Published by Elsevier Ltd.