Best flooring for Heat in kitchen?

I live in North Dakota, and Well Right now its -18F So,It gets plenty Cold in the winter, Our kitchen is a addition of our house,Which means it doesnt have a basement under that part of the house,The floor Out there is VERY cold VERY cold, Makes the room feel atleast 20 degrees Colder.We are going to redo the kitchen, The husband wants to put carpet out there to make the flooring and room feel warmer,We have 3 kids. NOT a good idea, So my question is, What type of Flooring out there will make it warmer, We have Basebord heat but it isnt seeming to be heating anything up floor wise, Now We need COST helpful stuff. Meaning Were getting appliances , Redoing the Cubbords, So the hubs says We have LITTLE left to spend on flooring.Any help would be FAB.