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We have studied theoretically and experimentally the effects of various types of nanoparticles (NPs) on the temperature stability range T BP of liquid-crystalline (LC) blue phases. Using a mesoscopic Landau-de Gennes type approach we obtain that the defect core replacement (DCR) mechanism yields in the diluted regime T BP(x) 1/(1 - xb) , where x stands for the concentration of NPs and b is a constant. Our calculations suggest that the DCR mechanism is efficient if a local NP environment resembles the core structure of disclinations, which represent the characteristic property of BP structures. These predictions are in line with high-resolution ac calorimetry and optical polarising microscopy experiments using the CE8 LC and CdSe or aerosil NPs. In mixtures with CdSe NPs of 3.5nm diameter and hydrophobic coating the BPIII stability range has been extended up to 20K. On the contrary, the effect of aerosil silica nanoparticles of 7.0nm diameter and hydrophilic coating is very weak.