One thing I've learned from talking to my aunt after she moved to Phoenix, AZ was that in Chicago and the suburbs, it's not so much the heat but the humidity. She says that it feels cooler when it's 100 degrees in Phoenix than when it's 85° in the Chicago suburbs. The humidity makes it feel 15-20 degrees hotter than the same temperature in most other parts of the country.
Still, thanks for the advice. I'll take my bike on Monday as while I've been ghosted for the job I interviewed for, I did get a 1-day temp job via a temp agency tomorrow on LaSalle St.