The Young's modulus of elasticity, denoted as $E$, is a measure of the stiffness of a material. It defines the relationship between stress (force per unit area) and strain (deformation) in a material in the linear (elastic) portion of the stress-strain curve. As temperature changes, the interatomic distances and bonding energies within a material also change, affecting its mechanical properties, including its elasticity.

For most materials, as the temperature increases, the atoms within the material gain kinetic energy and vibrate more vigorously. This increased vibration results in a reduction of the forces between atoms, making it easier for the material to deform under a given load. Hence, generally, the Young's modulus $E$ decreases with increasing temperature because the material becomes softer and less stiff. Thus, the correct option here would be:

Option C: decreases

However, it should be noted that the exact relationship between temperature and Young's modulus can vary depending on the material type and its microstructure. While the general trend for metals and polymers is a decrease in Young's modulus with rising temperature, the rate of decrease and the temperature range over which this occurs can differ significantly between materials. Some advanced materials and composites may exhibit more complex behavior due to their unique properties.