Chicago is COLD in the winter. You can just forget about keeping your tile warm in an unheated room. Even with an insulating membrane under your tile the ambient air tempurature will still make the tiles feel very cold.
Because your floor is painted (maybe stained) I would recommend a paper underlayment (also called an anti-fracture membrane) installed over the slab. It comes in 3' x 100' rolls and is installed using standard carpet adhesive and a glue trowel. It similiar to the paper found under the plastic film of vinyl flooring. This membrane will also help to insulate the tile from the slab. Not that much though.
Install your tile over the membrane using a sanded latex modified thinset. I would recommend using a 3/8" deep 1/4" wide square notch trowel.
Tile over the face of your step LAST. Lay your floor tile out over the edge of the step so that enough room will exist for the all of the face tiles to fit in flush and square. Your step may not be square with your room or your tile. If you do it this way you can make your step square.
You can purchase the membrane at any tile supply warehouse.