A method for resolving inverse heat conduction problems using approximating polynomials is described. The coefficients are obtained by constraining the even-numbered spatial derivatives of the polynomial at two points within the domain using the heat equation. The result is a linear time-invariant system that can be implemented as a digital filter and is suitable for application in a real-time sensor. The method places no restrictions on boundary or initial conditions, and temperature dependence of transport properties is accounted for in an approximate way. The performance of the model has been validated using analytical and numerical solutions, and results are presented in the frequency and time domains for several orders of polynomials. A propagation of error analysis is presented and is used to establish the optimum location of the sensors. Nomenclature a ij = matrix of location-dependent coefficients, a 13 , a 14 :m 2 ; a 21 , a 22 :m 1 ; a 23 , a 24 :m; a 43 , a 44 :m 1 b j t = vector of temperature measurements, b 1 , b 2 :K; b 3 , b 4 :K=m 2 c i t = vector of temperature profile polynomial coefficients, c 1 :K; c 2 : K=m; c 3 :K=m 2 ; c 4 :K=m 3 c p = heat capacity, J=kg K Im = imaginary part i = imaginary number, 1 p k = thermal conductivity, W=m K P n = temperature profile polynomial of degree n, K q = heat flux, W=m 2 Re = real part T = temperature, K _ T = rate of change of temperature, K=s t = time, s x = distance from the surface, m = thermal diffusivity, m 2 =s j = low-pass filter coefficient for time derivative, s 1 = gain, nondimensional j = low-pass filter coefficient for time average t = time step, s = uncertainty = density, kg=m 3 = length scale parameter, m 1 = phase angle, rad ! = angular frequency, rad=s j j = amplitude Subscripts i, j = polynomial and matrix indices m = low-pass filter index n = order of polynomial approximation for temperature 1 = position nearest to the measurement surface 2 = position farthest from the measurement surface % = nondimensional number Superscripts = frequency domain quantity = low-pass filtered quantity = complex conjugate