Preparation of the diluted acid can be dangerous due to the heat released in the dilution process. To avoid splattering, the concentrated acid is usually added to water and not the other way around. A saying used to remember this is "Do like you oughta, add the acid to the water". Water has a higher heat capacity than the acid, and so a vessel of cold water will absorb heat as acid is added.
Also, because the acid is denser than water, it sinks to the bottom. Heat is generated at the interface between acid and water, which is at the bottom of the vessel. Acid will not boil, because of its higher boiling point. Warm water near the interface rises due to convection, which cools the interface, and prevents boiling of either acid or water.
In contrast, addition of water to concentrated sulfuric acid results in a thin layer of water on top of the acid. Heat generated in this thin layer of water can boil, leading to the dispersal of a sulfuric acid aerosol or worse, an explosion.
Preparation of solutions greater than 6 M (35%) in concentration is dangerous, unless the acid is added slowly enough to allow the mixture sufficient time to cool.  Otherwise, the heat produced may be sufficient to boil the mixture.  Efficient mechanical stirring and external cooling (such as an ice bath) are essential.
Reaction rates double for about every 10-degree Celsius increase in temperature. Therefore, the reaction will become more violent as dilution proceeds, unless the mixture is given time to cool. Adding acid to warm water will cause a violent reaction.
On a laboratory scale, sulfuric acid can be diluted by pouring concentrated acid onto crushed ice made from de-ionized water. The ice melts in an endothermic process while dissolving the acid. The amount of heat needed to melt the ice in this process is greater than the amount of heat evolved by dissolving the acid so the solution remains cold. After all the ice has melted, further dilution can take place using water.