Let yourself cool down/air dry for a few minutes after arrival, before you even attempt to wash up. It seems counter-intuitive, but I find if I rush to wash my face, I keep sweating. I wash my face with a a travel sized bottle of my normal face wash and re-apply moisturizer w/sunscreen and any make up. I either use a small hand towel I carry, with regular soap from a rest room to do a spot wash (underarms, feet, neck), or I have, on some occasions used those bath cloth things you can heat up in the microwave if there's no water alternative. Some people use baby wipes.
When I had a longer (14 mile) hilly commute, I had very short, spikey hair. I just rewet it and put some gel in. My hair is still short, but is longer and requires more styling now. But, my commute to work is 5 miles, all downhill/flat. It's been fine so far, but I know I will be a bit sweaty in the coming months, as I am a head sweater! I just had it cut a little shorter, so the underneath part isn't as thick. I also have a very small flat iron, that I keep at the office. Just in case.
2015 Trek Silque SSL
Specialized Oura
2011 Guru Praemio
Specialized Oura
2017 Specialized Ariel Sport