‘Seven people died, while three were poisoned by the fumes and hospitalised,’ the emergencies ministry's branch in the oil-rich Tyumen region said.
The suspected cause was a short-circuit in an electric heater, used to warm the container which was lined with wood and insulation to keep out the cold, Russia's Investigative Committee said.
Regional prosecutors said all victims were citizens of Tajikistan, an impoverished ex-Soviet Central Asian country from which many people seek low-paid labour jobs in Russia.
The container was located at a construction site for a poultry farm.
In January at least 12 migrants from Central Asia, including three children, were killed when a fire at a sewing workship in Moscow caused its roof to collapse.
In August, 16 people, mostly women from Kyrgyzstan, were killed in a fire at a printing warehouse that started due to a faulty lamp.