By no means a warm-up, but the rest of the week is not as cold.
Overall, Tuesday temperatures will run about 5 to 10° warmer than Monday afternoon. Expect sunshine and enough of a breeze for cold morning wind chill values.
Overnight temperatures will stay mainly in the single digits above and below zero across Eastern Montana and northern Wyoming. Expect increasing clouds through the evening.
Clouds increase Wednesday, with highs mainly in the teens with some 20s in the mountain foothills and northern Wyoming. Scattered snow showers will develop in the mountains, and from Billings to the West and South.
The best chance of accumulating snow is late Friday through Saturday morning. Otherwise, expect high temperatures in the upper 20s to mid 30s, and most of the overnight lows into the teens to around 20° through early next week.
By now, average temperatures would normally be in the mid 40s. Expect colder than average temperatures through at least mid-March thanks in part to the snow on the ground.