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Curing temperature affects significantly the compressive strength development of mortar mixtures. Higher curing temperatures accelerate the cement hydration and thus also the early age compressive strength development. However, the age conversion factors in maturity functions, especially that of the Nurse-Saul function, are not sufficient to account for this acceleration and thus an additional “acceleration” factor is needed. The “acceleration” compresses a certain percentage of hydration or strength development into a smaller time interval. The strength development rate was increased because of the “compression” of the hydration. The “acceleration” factor was not equal to the “compression” factor. The reaction at the higher temperature was therefore less efficient in contributing to the compressive strength than the reaction at the lower temperature. A relationship between concrete strength and the Nurse-Saul maturity index combined with an “acceleration” and a “temperature efficiency” factors are used in an iterative procedure for predicting/estimating the strength development for other than the standard 20 °C curing temperature. Keywords: Curing temperature, Compressive strength, Maturity function, Activation energy