That's a lot of real estate--west of the Mississippi, east of LV. Perhaps some generalities first.
I assume you're primarily interested in undeveloped natural hot springs as opposed to developed natural hot springs. The former will be either a hike-in or a drive-up while the latter will almost always be street vehicle accessible with the spring waters captured and piped into a pool of some sort, with changing rooms, etc, and fee-paid use. In fact, the waters at Hot Springs, AR, Hot Springs, NC, and Warm Springs, VA are all examples of developed natural hot springs. And none are particularly hot, running right at 98-100 degrees. That's because all of the Eastern and Southern US hot springs are geothermal gradient hot springs as opposed to "hot igneous rock" hot springs as so many of the Western US hot springs are. Some of the hot springs in NV and WY emanate at temps in excess of 160 degrees F.
In any event, there are, to the best of my knowledge, no natural hot springs in the entire Midwestern US. The Midwest lacks young hot rocks to serves as a heat source within the water table's relatively shallow depth range and lacks folded and faulted mountains which provide a plumbing system allowing a steady flow of groundwater from high elevations to points deep enough in the crust such that the natural temperature gradient heats the water to something a little in excess of 100 degrees F, and then provides pathways for the water to reach the surface without having lost all of the heat picked up at depth. A geothermal gradient source generally must be in excess of 3,000' below the surface, so some mountainous topography helps to provide a high elevation recharge area and a lower elevation spring emanation point. Hot Springs, NC and Warm Springs, VA are surrounded by mountains topping out between 2,000 and 3,500' higher than the springs' emanation.
So, we're talking hot igneous rocks, and for hot rocks you've got to get to the younger mountains of NM, CO, and WY, each state being liberally peppered with natural developed and undeveloped hot springs. Perhaps the best way to get a read on the wheres, whats, and hows is via a guidebook. There are Falcon Guides titled for CO alone and one for MT and WY together. Jayson Loam has several titles a regional focus, including one for the Southwest, likely including NM and AZ. Lastly, you'll find lots of good info at
www.soakersforum.com and
www.hotspringsguy.com. I very happily "discovered" Sharkey's HS (developed, but lightly so) and Gold Bug (undeveloped, and a gem if there ever was one) in Idaho, each near Salmon, ID, from some Interwebs surfing which brought me to text, pics, and videos of the two hot springs.
Have fun!
Foy