The heat (enthalpy) of fusion in the CGS system is measured in ergs, and it is 1 (g-cm^2)/s. In the SI system, the enthalpy of fusion is measured in Joules. 1 erg is 10^-7 Joules.
The enthalpy of fusion of 1g of water is 334 Joules, which is 334 x 10^7 ergs