William Middleton was described by his lawyer as a "working family man" who had consistently denied killing nine-month-old Annalise.
But the Crown said that there was enough "circumstantial evidence" for the jury to convict.
Middleton, 33, is accused of murdering his daughter last September by setting fire to materials in his house at Brae in Shetland, with the smoke overcoming her.
In his closing speech at the High Court in Aberdeen, advocate depute Jock Thomson said experts had previously stated that two fires had been deliberately started in the house. He added that, other than children, Middleton was the only person there when the fire took effect.
But Jack Davidson, QC, for Middleton, said his personality would have had to "morph" to carry out the crime.
The trial, before Lord Kinclaven, continues today.