The algorithm used in this study to simulate hourly air temperatures from measured maximum and minimum air temperatures was based on a modification of the Wave algorithm. As with many, but not all algorithms of this nature, it was assumed that the hourly air temperature followed a sinusoidal curve. The current day was divided into three segments; from midnight to sunrise, from sunrise to the time of maximum temperature (which was assumed to occur at 2pm local standard time), and from this time to midnight. Four variables were used in the calculation of hourly air temperature; the current hour, the time of sunrise, the daily average temperature, and the difference between the daily maximum and minimum air temperatures (amplitude). In the modification to the Wave algorithm, if the difference between the previous day's and the current day's average air temperature was greater than one degree C, then the amplitude was multiplied by 0.7. This modification was based on evaluating hourly air temperatures for the year 2004 from Mead, NE. Independent data for this study was from 2003. The latitudes of the eight locations used in this study varied from 25.5 to 47.78 degrees and the longitudes varied from 80.5 to 124.15 degrees. The annual mean maximum temperatures ranged from 12.8 to 28.6 C and similarly for the minimum temperatures, from -0.5 to 18.6 C. Relative to the modified Wave algorithm, the percent improvement ranged from 3.4 to 12.2 percent. The root mean square error ranged from 1.2 to 3.2 C. As the difference between the average annual maximum temperature and minimum temperature increased, the root mean square error increased.