I think it would be fine on the floor. What is really important is to keep it away from drafts and possibly exterior walls, but mostly if there are drafts. The easiest way to check is to light a lighter or match where you will have the cage and see if the flame flickers as it would in a draft. Flames are very draft sensitive. With carpet and being on an upstairs floor, I don't think your floor could really be considered "cold".
Now, where to get the supplies?? Just wanted to let you know I found the best deals at Home Depot. they had a double pack of cubes, Rubbermaid "6pack" for 29.99, and at my local Home Depots, Coroplast 4x8 sheet for 17.98. Sabriel found a art store in Toronto that has Choroplast for under 14.00, so call a few art stores or sign shops, but if all else fails, it isn't a horrible price. Micheals sold 20"x30" sheets, about the size of bristol board for $9.00 a piece!
Walmart sells 3 pack cubes for 19.99 a 3 pack has just enough to make the walls for a 2x4, but no loft, no lid, no supports, nothing. One thing you may want to consider is look through the gallaries and Cavy Cage Superstar thread, and you will see elevated cages with storage underneath. Very cool.