At about 1.30 am on Sunday morning, a 25-year-old man woke to discover a fire in his home in Torduff Road, Gretna.
He was able to douse the flames and extinguish the fire and did not sustain any injury.
Detective Sergeant Hugh McCombe said: “Thankfully the man was able to put out the fire and damage to the house was limited to the front door area.
“However, had he not woken up and tackled the fire this could have been so much worse.
“He didn’t think to call the police or fire at the time as he had managed to put the fire out himself.
“However, on reflection he called police to advise later in the week.
“We know from our joint investigation with Scottish Fire and Rescue that this fire was deliberately set but a motive has still to be established.
“I am appealing to anyone who may have seen someone hanging about the area they did not recognise, or who may have any information about the attack to come forward to police.”
Anyone with information about the incident should contact Dumfries CID via the non-emergency number 101 or Crimestoppers on 0800 555 111 where details can be given in confidence.