Specific gravity:
- Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water).
- It is a dimensionless quantity and does not depend on temperature.
- Therefore, it does not increase with the rise in temperature.

Kinematic viscosity:
- Kinematic viscosity is the ratio of dynamic viscosity to the density of a fluid.
- It is a measure of a fluid's resistance to flow.
- Kinematic viscosity generally decreases with the rise in temperature.
- As temperature increases, the kinetic energy of the particles in the fluid increases, leading to faster movement and reduced resistance to flow.
- Therefore, kinematic viscosity increases with the rise in temperature.

Thermal conductivity:
- Thermal conductivity is the property of a material to conduct heat.
- It is the rate at which heat energy is transferred through a material.
- Thermal conductivity generally increases with the rise in temperature.
- As temperature increases, the kinetic energy of the particles in the material increases, leading to more collisions and faster heat transfer.
- Therefore, thermal conductivity increases with the rise in temperature.

Thermal diffusivity:
- Thermal diffusivity is a measure of how quickly heat can diffuse through a material.
- It is the ratio of thermal conductivity to the product of density and specific heat capacity.
- Thermal diffusivity generally increases with the rise in temperature.
- As temperature increases, the kinetic energy of the particles in the material increases, leading to faster diffusion of heat.
- Therefore, thermal diffusivity increases with the rise in temperature.

Conclusion:
- Among the given options, specific gravity is the property of air that does not increase with the rise in temperature.
- Specific gravity is a dimensionless quantity and does not depend on temperature. It is determined solely by the ratio of the densities of the substance and the reference substance (usually water).