Major meteorologists expect that the cold wave has not ended and Friday and Sunday will be colder than Thursday.

Temperatures reached -40 degrees Celsius last time in Edmonton was in 1972. We have a potential chance to reach this temperature or colder in the coming days, especially on the mornings of Saturday and Sunday.

The meteorological center at Edmonton International Airport has reached -40 degrees Celsius or colder in recent years, but it is outside the city limits, and no center in the city has reached -40 degrees Celsius since we reached -41.1 degrees Celsius on January 26, 1972.

The coldest temperatures in January in the past fifty years in Edmonton are:

-37.8 degrees Celsius on January 19, 1996 and -36.7 degrees Celsius on January 16, 2020, and it is very likely that we become colder than that.
I think the temperature will remain steady around -28 degrees Celsius during the day in Edmonton, but the winds at 10-15 km/h will lower temperatures in the range of -35 degrees Celsius to -40 degrees Celsius, and wind speeds will decrease to about 5-10 km/h from Friday to Sunday. So, the weather will not be cold all day.
But even at these wind speeds, wind chill will sometimes reach the range of -40 to -50:

-30 with wind 5 km/h = wind chill -36

-30 with wind 10 km/h = wind chill -39
-40 with wind 5 km/h = wind chill -47

-40 with wind 10 km/h = wind chill -51
Temperatures are likely to range between -40 degrees Celsius to -45 degrees Celsius on the mornings of Friday, Saturday, and Sunday outside Edmonton.
In the city, the temperature will reach -36 degrees Celsius on Friday morning, then -40 degrees Celsius on the mornings of Saturday and Sunday.

However, there is a very optimistic chance, with typical final results indicating a lowest temperature of -49 degrees Celsius and a peak of -40 degrees.