Thanks for posting - it does us all well to think about these things once in a while. However, just because I'm sitting at a computer with a physical properties database on it
:
0 degC, +10 degC +20 degC
Petrol Density, kg/m3 763 754.3 745.5
Diesel Density, kg/m3 856.9 843.2 836.3
So that gives a density difference of *roughly* 1.2% for petrol, and 0.8% for diesel for a 10 degC temperature rise. So I guess for a £50 fill of your tank, you might theoretically save £60p. However, i'd have thought it's highly unlikely that the temperature of an underground storage varies by anywhere near that much over the course of a day, so in practice, I shouldn't think it's worth losing much sleep over.
The thing about filling up when half full is a bit strange though, as that means that you're always carting half a tank's worth of petrol around with you that you never use, and I'm sure that will have just as big an impact as any vapour generation!
Actually, the thing that makes the biggest difference is how you drive, how fast you drive, the roofrack you left on, and how much cr@p you keep in your boot!!