1 If you are thawing salmon that was frozen in a block of ice, run cold water over the fish until all the ice chunks are removed. 2  Then cover the fish in plastic wrap, place it in a pan and leave it in the refrigerator for 6 to 12 hours.. Put the bowl on a flat surface in the refrigerator, away from foods that will soak up the smell of the salmon. The refrigerator should be kept between 35 and 40 degrees Fahrenheit (1.7 to 4.4 degrees Celsius), in order to inhibit the growth of micro organisms.