The Belgium-flagged vessel overturned off the Kent coast at about 23:00 GMT on Tuesday, the BBC understands.
One person - spotted clinging to the upturned hull of the boat - was rescued almost nine hours later, at 07:30 GMT.
Kaimes Beasley, of Dover Coastguard, said it would be possible to survive in the water for about 15 hours.
Two helicopters, including one from the Belgian search and rescue service, plus three lifeboats have been involved in the search.
The operation was called off late Wednesday afternoon due to fading light, Ramsgate lifeboat said.
Mr Beasley said: "Weather conditions overnight were relatively benign, winds were not terribly strong and the sea had been calm.
"Either way, it is still the North Sea in the winter and would have been very cold.
"In the southern North Sea, water temperature is about 9.5C and the air temperature less than that.
"There is a significant risk in terms of hypothermia."
The emergency services were first alerted at daylight when a passing boat saw the upturned vessel with one of the crew members standing on it.
He was able to tell them that two of his colleagues were unaccounted for.
Earlier, two divers and a doctor from Belgium were lowered on to a Ramsgate lifeboat to join the search for the two missing fishermen.
The operation is focussing on an area just up the coast from here in an area known as North Foreland.
That is where the lifeboats were searching for much of the morning and continuing into the afternoon.
A search for two missing fishermen who disappeared when their boat capsized in the English Channel has been called off for the day.