The fuel density/volume/temperature vs. $ problem isn't that significant in an automobile with small tanks (13-26 gallon tanks), but you can make money if you routinely fill up during the coolest part of the day. Your tank will be cooler and allow for more volume of gas too. But, it's probably not a good idea to let that full tank sit for the remainder of the day while it starts to expand.
While flight planning in the Navy, fuel density was a critical variable that we used for take-off weights, cruise altitudes, various ranges we could fly, and what alternate airfields we could use if there was a problem at our final destination.
Here is a quote from an old P-3C NATOPS manual on fuel density vs. temperature:
For accurate mission planning, the combined effect of initial fuel density and temperature must be considered for the fuel onboard. Assuming the fuel being used has an initial fuel density of 6.3 pounds per US gallon at 15C/58F (standard day), the same fuel at a temperature of 40C has a density of 6.15 pounds/gal. For an aircraft with 9,200 gallons of fuel, the load would be 56,580 pounds as compared with 58,510 pounds for nominal JP-4 at the same temperature. (JP-4 is the least dense with the lowest flashpoint of the military jet fuels. JP-5 and JP-8 are the others. JP-5 has the highest flashpoint/highest density/lowest BTU's of the 3 and is used for shipboard ops).
This extra 2,000 pounds of fuel would give me an extra 30 minutes of flight time if I needed it. That's why I always preferred early morning pre-flights for long missions. My experience with flight planning shows the OAT vs. density conversion table we used was fairly accurate. I think the ambient temperature of the aircraft fuel tanks and the already existing ramp load warmed up the incoming fuel very rapidly.
The density vs. temperature ratio is linear for all 3 JP's, so I would expect gasoline and diesel fuel to be of similar weights and ratios.
I hope this adds something to the discussion, or maybe I just found my old NATOPS manual for nastalgia! That's OK too.