How likely is a frozen copper water line to burst when defrosted?

The cold water line to the kitchen sink is frozen solid this morning. No water comes out when the valve is turned on. I’ve opened the cabinet doors to let warm air from the house in. The plumber can’t get here right away, and checking things in the basement, the shutoff valve for that line is upstream of the boiler, so if I close it, the radiator heat goes off making things much worse.

Questions. Should I set up a portable bathroom heater to blow warm air into the cabinets? Would that make the line more or less likely to burst upon defrosting. How likely is the copper water line to burst during thawing.