With the price of fuel at historic highs, every bit of savings you can get at the pump helps your bottom line. One piece of advice often dispensed is to fill up in the morning when it's cool rather than in the heat of the day. This is because gasoline, like most liquids, expands when the temperature is raised, so when it's cooler, the gasoline is more dense, or heavier, and you get more gasoline per gallon.
First of all, the volume of gasoline, diesel and other oil-derived liquids are calibrated to a temperature of 60F (15C). The Canadian government has published a helpful chart of the volume correction factors for gasoline; on this chart the correction factor 1.0000 can be found for T=15.0C. When the temperature dips to -20C (-4F), the correction factor is 1.0444, so a gallon of gasoline at that temperature will get you 4.44% more mileage than at 60F.
Because this is a Canadian chart it goes to -40C (-40F), but I'd really rather not think about filling up under such circumstances. On the other hand, the chart only goes to 30C (86F); for temperatures higher than that you need to consult a US publication; the one I found is a 1920 publication in the Journal of Industrial and Engineering Chemistry. Its data is consistent with the Canadian data from 2011 but it does go to 120F (49C), where the volume correction factor is 0.95 - 0.97 (compared to the standard at 60F). You can buy an app for this - but my phone doesn't do apps so I get to stare at the tables.
The tables suggest that, if you live in Tucson where the temperature swings are large, you can get about 5% more gasoline if you go to the pump at 4am (the coolest time of day) rather than the 3pm school pickup time. Sounds great.
However, before you set your alarm for such an ungodly hour, you might consider that the gasoline at the station is generally stored in an underground tank, where the temperature is much more steady than at the surface.
Just think: in the summer your basement is always cooler than the rest of the house. And the water coming out of your tap (once you're run it for a while) is nice and cool: it is at the temperature of your well, or your municipal water pipes, both underground. (Conversely, in wintertime your water keeps flowing despite freezing air temperatures, because the pipes remain above freezing).
In fact, once you're 5-6 meters (15-18ft) below the surface, the temperature of the ground is a steady 45F (8C), fluctuating by at most 2C in response to temperature swings at the surface (this is what makes geothermal home heating / cooling work). So the volume correction factor inside the storage tank is at most about 0.5%. While the first quart or so that gets pumped into your car tank is at the surface temperature, the rest is close to the temperature of the storage tank, much like your tap water is still cool in the summer.
Just to be sure, pumps in Canada are outfitted with a temperature correction device, so that each litre dispensed by the pump means the equivalent of one litre of gasoline at 15C (60F), no matter what the actual temperature of the tank might be.
US pumps don't have this correction, but are you really going to lose precious sleep over savings amounting to at most 0.5%? That's $0.02 on your $4 per gallon gas. You'd do much better by choosing a gas sipper next time you're ready to buy a car, for some real savings at the pump.
Of course, CelloMom has her own list of strategies for increased fuel efficiency. Some are out-of-the-box. None involve getting up before dawn.