It is shown that the equation ΔE = αT2/(T + β), which is commonly used to describe the temperature variation of energy gaps in semiconductors, is a second order approximation of the electron–phonon interaction term in the recently proposed equation ΔE = UTs + Vθ[coth (θ/2T) – 1]. The calculation shows that the parameters α and β of the approximate equation can describe the characteristics of semiconductors only if the relation holds, with the validity limited by the magnitude of the existing dilation effect. In this case it is found that β = θ/2 where θ is the effective Einstein vibrational frequency, in temperature units, of the phonon spectrum in the material. A comparison of the two equations when fitted to experimental data is presented and discussed.