ACT Fire and Rescue were called to the fire on Thursday morning at 5am. The blaze, which measured about one hectare in size, was extinguished by 6.35am.

Witnesses at the scene told police they'd seen a man attempting to start a fire in the area.

Shortly afterwards officers located the homeless man who had suffered burns to his throat, chest and arms. The man was airlifted to Concord Hospital in Sydney due to the seriousness of his injuries, and will be helping police with their enquiries.

Police want to speak to the man about the Molonglo fire near Tuggeranong Parkway and Lady Denman Drive, and also about a grass fire on Wednesday in the same area - near Yarralumla Creek on Lady Denman Drive.

Officers are urging anyone who may have seen a man with a small white dog with black markings in the area before either fire, to contact Crime Stoppers immediately.

The fire near Yarralumla Creek on Lady Denman Drive on Wednesday afternoon burned through half a hectare.

Acting Officer-in-Charge of Woden Police Station, Sergeant Louise Denley, has asked anyone who has not yet spoken to police to contact Crime Stoppers.

"We are urging anyone with information on either fire to please call Crime Stoppers on 1800 333 000," she said.

"The man always has his dog with him, a small white dog with black markings. If you recall seeing a man with a dog around the time of the fires, please contact us.”

The ACT is under a Total Fire Ban on Thursday and heavy penalties will apply to people caught lighting a fire.

Crime Stoppers can be contacted on 1800 333 000 or via www.act.crimestoppers.com.au. Information can be provided anonymously.