This paper is aimed to fill the void in the literature regarding the temperature-dependent ideal tensile strength of the AlB2-like diborides. To this end, two models of temperature-dependent ideal tensile strength of hexagonal single crystals are developed based on the critical failure energy density principle and the critical strain principle. The two models relate the ideal tensile strength to the elastic properties, thermal expansion, and specific heat at constant pressure of single crystals. The temperature-dependent uniaxial ideal tensile strengths of ZrB2, HfB2, and TiB2 are predicted. The predictions from the critical strain principle agree well with that from the critical failure energy density principle. The study shows that the temperature dependence of the ideal tensile strength is similar to that of Young's modulus. That is, the ideal tensile strength firstly remains approximately constant and then decreases linearly as temperature increases. The fracture failure for hexagonal single crystals at elevated temperatures is identified as a strain-controlled criterion for the first time.