camp in Mae Hong Son province, with women, children and the elderly believed to make up the majority of the victims.
Rescue workers were on the scene at the remote mountainous camp area, Mae Hong Son provincial governor Narumol Paravat told AFP by telephone.
"The latest death toll we can confirm through military walkie-talkies is 42," she said, adding the toll was likely to rise further as rescue workers search the area.
Authorities believe the fire was sparked by an unattended cooking flame.
A local district official said hot weather, combined with strong winds caused the fire to spread quickly among the thatched bamboo shelters.
Police on Saturday said around 400 temporary homes had been incinerated, while the Disaster Prevention and Mitigation Bureau said a school, clinic and two food warehouses had also been destroyed.
The Thai government pledged an investigation into the fire at the camp, which houses roughly 3,700 refugees.
Ten camps strung out along the Thai-Myanmar border house a total of about 130,000 people, who first began arriving in the 1980s.
Many of the refugees have fled conflict zones in ethnic areas of Myanmar, also known as Burma.
Families often live cheek-by-jowl in simple bamboo-and-thatch dwellings.
Many of the camp residents have been registered with the UN as refugees, and an ongoing resettlement programme has allowed tens of thousands to move to third countries.
After a new quasi-civilian government replaced the long-ruling junta in Myanmar two years ago, Thailand announced it wanted to shut the border camps, raising concern among their residents.
But so far the displaced residents have been allowed to stay and the Thai government has stressed that it will only send them back when it is safe.
Many of the refugees are from Myanmar's eastern Karen state, where a major rebel group, the Karen National Union (KNU) signed a ceasefire deal with the new regime last year after decades of civil war.
Vast numbers of people fled the former Myanmar junta's counter-insurgency campaign, which rights groups say deliberately targeted civilians, driving them from their homes, destroying villages and forcing them to work for the army.
Years of war have left the Karen region littered with landmines while development has been held back, leaving dilapidated infrastructure and threadbare education and health services.
Hundreds of homes were destroyed at a different border camp in February last year by a fire that the authorities also blamed on cooking.