UPDATED: 3:16 p.m.

CHICAGO (CBS) — Chicago was in for another mild day on Tuesday, a day ahead of a winter storm system that could dump several inches of snow on parts of the Chicago area, particularly to the south and east.

Temperatures were expected to reach the low 40s on Tuesday, with a mix of clouds and sunshine. The cloud cover will continue to build into the afternoon.

Meantime, the National Weather Service has issued a Winter Storm Warning from Wednesday morning through late Wednesday night for six counties in Illinois including Cook, Will and Kankakee counties. The warningalso includes most of northern Indiana.

Snow was expected to begin falling late Wednesday morning, and continue through early Thursday.

The system will have a distinct line between areas that will get a lot of accumulation, and those that won’t get much at all. As of Tuesday morning, the heaviest accumulations were expected well south of Chicago, east of I-57, and in northwest Indiana, where totals could be between 3 and 6 inches. North of Kankakee, accumulations were more likely to be 1 to 3 inches. Further west, in areas like Rockford, totals could be less than an inch.

If the storm system shifts north and west, the heavier accumulations could hit the city, but if it shifts east, the Chicago area might not get much snow at all.

After the storm system pushes through, colder temperatures were expected Thursday and Friday, when highs will be in the mid 30s, before a mild weekend, with temperatures in the mid 40s on Saturday, and the high 30s on Sunday.