Insulating Carpet

[Michael Ting]

I bought my first condo in Chicago during summer and coming to a realization that the house can get very very very cold in winter. A little info on the unit. It is a one bed room condo, 800 square foot, located on the first floor. The floor has a "plywood" finish on top of concrete slab. The unit has gas water heater and forced air gas heater. Because walls are decently insulated, my suspicion is that a lot of moisture and cold just seep out of the floor. I don't think plywood finish is a very good insulator. On most days during winter, the room temperature is only about 10 degree higher than outside temp if there is no heat turned on. In summer, it is about ten degree colder than outside. Here is my question ...

Can I put on a removable carpet on top of the plywood finish of the floor? How much insulation would that add? and would that trapped coldness and moisture destroy the "plywood" floor?