I would not recommend walking through Northern Kansas in February/March, the average low in some of those areas is like 15 this time of year, and storms roll in pretty often.
Sleeping bag ratings don't mean anything especially when it's in the teens out and the air is damp. Add actually getting wet and most would find the setting to be unpleasant. Don't forget about wind, without some kind of windbreak, 32 is going to feel like 2 in that bag.
Realistically speaking it's a 600 mile trek on foot, with gear and fatigue, and exposure (it's actually a real thing, most of us get it in mild forms all the time and don't even realize it) by day 2 even a hardened backpacker would only be averaging 2 or 3 miles an hour, with dry and flat ground conditions. Say you put in a solid 8 hours of beating feet everyday, that's like 25 days of walking. There are more scenic month long hikes you can do.
Also, if you do decide to walk, don't walk on the freeway take less traveled back roads, resupplying will be a little more of a challenge, but I can guarantee your sleeps will be less noticed by watchful eyes and more comfortable.
At least it will be warming up by the time you reach Aurora
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I would certainly recommend reevaluating your feelings on alternate methods of travel besides walking. Research thumbing I-70 west.