To figure out how to improve the accuracy of the experiment, we'll need to know what the experiment was (materials, steps, etc.).
However, in general, you have to think of sources of error for this experiment. To find this, you have to recall what you're looking for when you're finding the molar heat (enthalpy) of fusion: the enthalpy gained or lost as a material turns into a liquid from a solid.
There are plenty of sources for error here! I'll highlight a few:
- Leakage of heat from the apparatus
- Thermometer delay
- Sensitivity if your measurements
Leakage of Heat
This is one that'll destroy your results, pretty clearly because if you do not capture the heat in the liquid whose temperature you're measuring (I'm assuming you're using an improvised calorimeter for this experiment), you measure a lower heat than what is actually released to (or taken up from) the environment.
Think of ways heat would get released to anything that is not the liquid whose temperature you're measuring. For example, when I did this experiment way-back-when, We used a cardboard top on a styrofoam cup. Heat could definitely leak out the hole in the cardboard, the sides of the cardboard, or even because the cup didn't insulate well! Plenty of data loss here.
If your thermometer does not change its reading quickly based on temperature, it may rise too little before the liquid whose temperature you're measuring starts being cooled or heated by the environment external to the calorimeter!
For example, suppose the temperaure of the water in the calorimeter has already reached 30 degrees C, but your thermometer is struggling to climb past, say 28. In the time your thermometer takes to rise higher, you water may have cooled to 29 degrees because of your lab's ambient temperature. As a result, you would measure 29 degrees instead of the true 30.
Sensitivity of Measurements
This is a big one here, depending on how accurate you want to be. Many lab thermometers only have every degree marked. Water, often the measurement liquid of choice, has a high specific heat, meaning its temperature won't change very much inresponse to heat input. Combine these two factors with a reaction that might give off only a little bit of heat, and you end up getting a measurement with too large of an uncertainty to be meaningful.
The solution? Get more accurate thermometers, get different fluids that change temperature more readily in response to heat, get more reactant for the calorimeter.
There are plenty of ways to fix calorimetry experiments. I only highlighted a few, but they tend to all revolve around making sure you capture all the heat generated in the fluid you're measuring, and making sure that you capture every degree of difference of the fluid once the temperature is at equilibrium throughout the fluid.
I'm sure you can find some more after this primer! Good luck!