Solvent and Solute Chemistry
Sugar is a solid solute, comprised of small crystal structures. Water is a liquid solvent. As sugar is added to room temperature water, a portion of the sugar volume dissolves into the water. As it dissolves, the sugar crystals absorb the heat. The dissolved sugar molecules effectively fit into the spacings between the water molecules. Once the spaces are full, any remaining sugar will not dissolve.
Le Chatelier's Principle
Le Chatelier's principle states that a stable system encountering stress will try and relieve that stress, effectively regaining its equilibrium. Heating water with the same sugar volume as the room temperature water will dissolve more sugar at a faster rate. The heated water is the stress on the system. The system will try and regain its equilibrium by dissolving more sugar since the dissolution process absorbs heat.
Alternative Dissolution Method
A solid can dissolve faster by exposing more surface area to a solvent, regardless of the solvent's temperature. Grinding sugar crystals increases the solid's surface area. As a result, more sugar will dissolve with the excess surface area exposure, especially if the mixture is stirred. However, adding heat to the ground solid will increase the dissolution rate even more than just exposing the surface area. The rate increase would depend upon the heat's temperature, sugar amount and water volume.
Observing Dissolution
If you are performing a science experiment for students to observe solid dissolution, then use a solvent that is clear. Using basic coffee will not give the students a view of the dissolution process. Use water, club soda or even rubbing alcohol for viewing solid dissolution.