Using more than three times as many stations and times series of daily data that are generally 1.5-3.0 times longer than those in a previous study, estimates of the natural variability, also known as climate noise, of surface air temperatures are extended over most of North America. The potential for long-range prediction of monthly means is determined by comparing the actual interannual variability of monthly means with the climate noise that is assumed to be unpredictable at long range. The climate noise estimates are typically larger during winter than during the other seasons. Nonetheless, the potential for long-range prediction is, generally, greatest for January and least for April. During January, temperatures nearest the oceans are more predictable than those for the central portions of North America. The low-frequency white-noise statistical model that is used to estimate the unpredictable climate noise is compared with times series of (near) surface temperatures from a general circulation model to confirm its credibility. The estimates of the potential for prediction are tested further to establish their sensitivities to a critical parameter of the statistical model and to spatial averaging.