The largest is Montana which has a range of 187 degrees F between its state-wide record max of 117 and record minimum of -70. Utah is close behind with a range of 186 degrees.
And with a range of only 88 degrees is the state of Hawaii where the all-time maximum is 100 degrees and an all-time minimum of 12 degrees (on the summit of Mauna Kea).
See http://ggweather.com/climate/extremes_us.htm.