1 Kelvin and 1 degree Celcius share the same magnitude.
The only difference between the Kelvin and Celcius scale is that the Kelvin Scale is absolute, ie. all measurements in Kelvin are always positive.
In terms of temperature, 0K = -273.15 degree celcius.
If the website gives you the heat capacity in terms of mole and not gram, just convert it from a molar basis to a mass basis. 1 mole of Copper is equivalent to 63.546g.