How to set and give a fixed reference temperature in the calculation with the Buossinesq approximation? Is this temperature random? Will it affect the results?

thank you

your reference values are the free stream state values in general or any other state that you consider not changing (That depends on your particular problem). What Random does mean in your question?

Just make sure T_ref is less than the minimum temperature in your solution domain. Otherwise you'll get strange (and incorrect!) reversed flow regions.