Probably not too much.  The compressor will have to work a little harder over the time it takes to get the temperature down to the refrigerator's operating range.  A possible concern would be the surrounding food warming up as it absorbed heat from the newly introduced dish.  A big factor in determining how much harder it makes the refrigerator work is the size of the dish.  A cup of hot liquid is going to hold less heat than a bubbling hot casserole just out of the oven.  Here's a fun little study of toasters in freezers in XKCD.