That's a strange experiment... there's no time related to the heat of fusion. The formula that gives the heat of fusion is:

Q = mL

Where Q is the quantity of heat, m is the mass and L is the specific latent heat (for melting, it is the specific latent heat of fusion).

So, L = m/Q

I would rather expect something like:

1. Take mass of water.

2. Take mass of ice cube.

3. Record initial temperatures.

4. Put ice in water.

5. Record final temperature of water as soon as all ice melted.

6. Q will then be obtained from Q = mcT for water (m is total mass of water, c is specific heat capacity of water, T is Tf-Ti (Final temp. - initial temp).

7. The use L = Q/m, you get Q from step 6 and m is mass of ice cube.