Measurement of the electron energy distribution in high temperature laser produced plasmas is discussed. The problem arises in thermonuclear fusion research with lasers, where strong enhancement of the high energy tail of the distribution may occur. It is shown that a method based on X-ray bremsstrahlung intensity, recorded as a function of metallic absorber thickness, is applicable in the energy range 1 to 40 keV. Two stages of deconvolution to obtain first the X-ray spectrum and second the electron energy distribution are considered. Simple semi-analytic methods of sufficient accuracy for experimental work are outlined and their regime of validity discussed.