What sort of driving are you doing when you see these temperature changes? Open road can see cooler running temperatures while town driving might show slightly higher temperatures depending on how the thermostat map is intended to function.
Now I am not sure about exactly how the engine in the 320i works in terms of temperature range and management, but this is what the N52 in the 330i does:
The N52 has four different temperature ranges that can be implemented:
• 112°C ECO mode (economy)
• 105°C Normal mode
• 95°C High mode
• 80°C High + mapped thermostat mode
The coolant control sets a higher cylinder head temperature (112°C) if the engine control unit determines ECO mode based on the current operating conditions.
The engine is operated with relatively low fuel consumption in this temperature range as the internal friction is reduced.
An increase in temperature therefore favors lower fuel consumption in the low load range. In HIGH and mapped thermostat mode, the driver wishes to utilize the optimum power development of the engine. The cylinder head temperature is therefore reduced to 80° C.
This results in improved volumetric efficiency, thus increasing the engine torque. The engine control unit can therefore set a certain operating mode adapted to the respective driving situation. Consequently, it is possible to influence fuel consumption and power output by means of the cooling system.
This above taken from a detailed online available N52 spec PDF.