Pressure: 
Pressure considerations are critical, especially in elevated tanks or underground tanks. The pressure exerted by the water column (due to its height and density) affects the design of the tank walls, base, and roof. It influences the thickness of the walls and the reinforcement needed. 
Temperature:
While temperature is important for the thermal expansion and contraction of materials, it is generally not a primary design factor for the structural aspects of the tank compared to volume, pressure, and weight. It becomes more relevant in regions with significant temperature variations or when using materials sensitive to temperature changes, such as certain types of plastics. 
Volume:
The volume of the tank is a primary factor since it determines the capacity of the tank to store water. It directly impacts the size, dimensions, and layout of the tank. Volume is crucial in ensuring that the water storage meets the demand requirements. 
Weight:
The weight of the water and the tank structure is essential for designing the foundation and ensuring structural stability. The tank must be able to safely carry its own weight when filled with water. The dead load (tank's own weight) and live load (weight of water) are critical considerations. 
Conclusion 
The factor that is not as necessary (or not a primary factor) in the structural design of a water tank, as per standard design practices, is Temperature.