At 8:40 p.m. on December 13, two men boarded the train at Colchester North and during their journey, lit a small bit of paper and stamped out the fire.
They then lit a large pile of paper on the train seats and ran off the train at Witham just after 9pm.
A member of the public tried to stamp the fire out with his feet but it had to be tackled by a member of staff with a fire extinguisher.
Investigating officer PC Steven Smith said, “The people who did this may have found it funny, but it was an incredibly reckless and stupid thing to do.
“They had no idea how big the fire could have become and it was only because a member of the public spotted the fire and alerted staff so quickly that it was extinguished before anyone was hurt.
“We want to speak to the two men in these images as we think they will be able to help with the investigation.”
Anyone with information is asked to contact British Transport Police on 0800 40 50 40 or text 61016, quoting 317 of 11/1.