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Petroleum expands with temperature, so density measured hot must be corrected to a reference temperature — 15 C internationally or 60 F in North America. The correction is density x (1 + alpha x temperature difference), with alpha around 0.0007 per degree for middle distillates and 0.0009 for gasoline.
Density correction
Density at reference = observed density x (1 + alpha x (T_observed - T_reference))
API gravity
API = 141.5 / SG at 60 F - 131.5
Custody transfer measurement must use the volume correction tables prescribed by the applicable measurement standard and contract.
A tanker loaded at 40 C and discharged at 15 C contains the same mass but different volume. Correcting to a standard temperature is the only way volumes can be reconciled and taxed consistently.
The API MPMS Chapter 11 tables, or the ASTM D1250 volume correction factor tables. Simple linear expansion is adequate for estimation but not for custody transfer.