Which units do I use in calculating heat capacity?
Yes, you would have to change it to grams. 

Units must be consistent. Specific heat is defined as the energy required to raise one gram of water by one kelvin. At atmospheric pressure in a closed container, the specific heat of water is 4.184 joules. 

One mole of water is 18.016 grams. So: 

$E =mc \Delta T $

Where $m$ is the mass of the water, $c$ is the specific heat capacity of water, $\Delta T $ is the change in temperature, and $E$ is the energy required. Substitute in your numbers, and you shall get the right answer:

$E = (18.016\ \mathrm{g})(\frac{4.184\ \mathrm{J}}{\mathrm{g\ K}})(363\ \mathrm{K} - 293\ \mathrm{K})$

$E = 5280\ \mathrm{J}$

If you wanted to use moles directly instead of converting to grams, you would have had to use the molar heat capacity. Generally, people prefer to use specific heat. Engineers sometimes use the volumetric heat capacity as well.