Speaking after today's hearing Solicitor General Oliver Heald, who referred the sentence to the Court of Appeal for review, said: "It is hard to overstate the seriousness of this crime."
Carl Mills has had his sentence for killing three members of the same family in Cwmbran increased from 30 years to 35 years by Court of Appeal Judges.
The court had heard how Mills bombarded his partner with texts and warned "I will burn your house down".
Kimberley, born 13 weeks premature, was at home for the first time after being discharged from hospital on the day of the fire.
Homeless Mills, the baby's father, was living in a tent in the front garden but had been banned from seeing the child unsupervised.
A man who burnt down his teenage girlfriend's home, killing three generations of one family, is having his sentence reviewed to see if it is "unduly lenient".
Carl Mills was jailed for life in July and ordered to serve a 30-year minimum term behind bars before he can apply for parole.
46 year old Kim Buckley her 17 year old daughter Kayleigh and 6 month old granddaughter Kimberley, died in the fire in Cwmbran last year.
The 30 year minimum term imposed will be scrutinised at the Court of Appeal in London.
28 year-old Carl Mills has appeared at Caerphilly Magistrates Court this morning charged with three counts of murder.
It follows the death of Kim Buckley, 46, her daughter Kayleigh, 17, and six-month-old granddaughter Kimberley who were found following a fire at their home on the Coed Eva estate in Cwmbran on Tuesday.
Following today's hearing Mills will appear at Newport Crown Court on Monday morning.
A 28-year old man has been charged with three counts of murder following a fire which killed 3 generations of the same family in Cwmbran on Tuesday.
Kim Buckley, 46, daughter Kayleigh, 17, and six-month-old granddaughter Kimberley died in the house fire on the Coed Eva estate.
Carl Mills will appear before Caerphilly Magistrates' Court later this morning