Totally possible! I live in CA, it doesn't get quite as hot here, but it's consistently 90-100+ in the summer. I get to campus ~15 minutes early to cool off. I use these:
wetones to clean sweat off. About a dollar for a pack of 20 or so. The biggest thing is just having enough time to cool off. It seems you're not riding in your work clothes, which is good. Changing helps loads. If you tend to stink a huge amount, you may consider reapplying deodorant to be on the safe side.