Malcolm Webster, 54, was jailed for a minimum of 30 years for killing Claire Morris, 32, in the planned crash in Aberdeenshire in 1994 and attempting to kill Felicity Drumm in New Zealand in 1999 to claim insurance money.
The former nurse, from Guildford, Surrey, was handed the life sentence after being convicted of the crimes in May 2011 following a five-month trial.
He lost an appeal against his conviction in December when judges at the Court of Appeal in Edinburgh rejected a claim that he was the victim of a miscarriage of justice.
Three judges will consider Webster's appeal against the length of his sentence at the Court of Appeal in the city on March 14.
Two of Webster's lesser convictions for fireraising were quashed in December.
Sentencing him in July 2011, Lord Bannatyne condemned his ''cold-blooded, brutal and callous'' crimes, driven by an insatiable appetite for money and which formed part of a fraudulent plot to pocket almost £1 million in insurance payouts.
The trial spanned five months, making it the longest murder trial against a single accused in Scottish legal history.
Webster claimed the death of Ms Morris was a tragic accident which happened when he swerved to avoid a motorcyclist.
The jury heard the killer drugged her before driving the car they were in off an Aberdeenshire road and starting a fire while she lay unconscious inside.
He fraudulently claimed more than £200,000 from insurance policies following her death, later spending it on a Range Rover car, a yacht and on seducing a string of women.
In 1999 he tried to murder Ms Drumm in a copycat car crash in New Zealand in an attempt to claim more than £750,000 of insurance money.
Police started investigating Webster's past when one of Ms Drumm's sisters contacted British police in June 2006 to report her suspicions about him.
After the investigation into Ms Morris's death was reopened in 2008, forensic tests on a tissue sample from her liver revealed she had been given a sedative before the crash.