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Expanded clay concrete (ECC) is a promising structural material for buildings due to its light weight and heat- and sound-insulating properties. Adding basalt fibers (BFs) in ECC reduces its brittleness and enhances its mechanical properties. The heat treatment (HT) of BF-reinforced ECC can significantly accelerate the strength growth during cast-in-situ construction, which allows the reduction of the turnover of the formwork and the construction period, as well as leading to lower construction costs. This paper presents an HT technology for load-bearing structures, containing a BF-reinforced ECC mix and using infrared rays for cast-in-situ construction. The issue of the strength growth of BF-reinforced ECC during HT has been studied. Microsilica and fly ash were added to the ECC mix to obtain a compressive strength of more than 20 MPa. Four different mixes of ECC with chopped BFs in the ratios of 1:0, 1:0.0045, 1:0.009 and 1:0.012 by weight of cement were studied. Test specimens were heated by infrared rays for 7, 9, 11, 13, 16 and 24 h. Then, the heat-treated specimens were tested for compressive strength after 0.5, 4, 12 and 24 h cooling periods. The analysis and evaluation of the experimental data were carried out based on probability theory and mathematical statistics. Mathematical models are proposed for forecasting the strength growth of BF-reinforced ECC during cast-in-situ construction.