We, city cyclists, like to say that there is no bad weather for cycling, only bad clothing. If it rains, wear a rain jacket, waterproof shoes, pants, etc. If its' hot, wear light, loose clothes and a hat (or a helmet, if you prefer).
Heat wave (Source: Google Images)
Just yesterday, I had a business meeting at work, which required me to wear a little less casual clothes than usual. Fortunately, the dress code was so called business-casual, which means that a full suit and a tie was not required. Light suit pants and a shirt was enough. I wrote "fortunately", since this week we have a typical New England summer in Boston: very high humidity and air temperature of 35deg C (95deg F). And this is where I am getting to the point of this post. Is bicycle good for any weather if situation requires you to wear business attire?
I can't imagine riding a bike in a weather like yesterday, wearing a full business suit. There would be no way not to get sweaty. The only solution would be to pack the suit in a bag, attach it to the bike (not trivial - suit bags are large), wear something completely different (shorts and a t-shirt), and change after getting to work (perhaps after taking a shower). But then, why bother? It would be easier to either drive (A/C on, please) or take a bus (hopefully the A/C is on). I think it gets actually easier in winter - you may be cold a bit if you dress too light, but not sweaty. Even in a suit.