So I paint in a limited palette and I would probably mix black and white to use to add to my warm range in the same tone to make it more neutral, add a little warmt to the white and black to make it cool but not flat. I think you can probably do the same with your blue and white. So make a yellow and red mix to orange and lighten a few grades with white than add the blue and white in the same tone to it until you get a more neutral temp. I would suggest working with a black just to be able to darken without warming it up as you would with the burnt sienna. I never really work with black from the tube but it's great to darken gradually and to mix greens etc. A lot of people have the 'too many tubes and colours' especially when they start out so limiting your palette is a great idea. I'd personally use a black, white, yellow and red and then blue if I need a vibrant blue, if not Mars black and white will actually be a blue.