In this work we discuss effects allowing local habitability of some extraterrestrial planets of low average surface temperatures. We analyze the problem of diurnal and seasonal changes of temperature and biological productivity at different locations on a hypothetical Earth-like planet. We have found, that under some circumstances the temperature may locally rise well above the average value, allowing periods of enhanced biological activity. In this way, bioproductivity can become periodically possible on a planet that has an average temperature clearly below 0°C. Such thermal conditions are encountered on Mars (Smith et al. in Science 306:1750–1753, 2004) generally considered as inhabitable. In reality, an appropriate temperature is not sufficient for habitability. The presence of liquid water at the considered location is also necessary. We discuss how temperature oscillations affect habitability in the framework of a conceptual model. We find that the considered effect of diurnal and seasonal temperature oscillations can extend the outer boundary of the habitable zone up to 2 AU, while global average temperatures are below 0°C for heliocentric distances R h > 1.12 AU (dry atmosphere, low CO2 pressure), or R h > 1.66 AU (humid atmosphere, high CO2 pressure).