You may want to look into buying clothing specifically marketed as keeping you cool. I regularly ride my bike 15 km in 30 C heat. In a white cotton tshirt, sweat runs down my arms and I have trouble gripping the handlebars. In a long sleeved "performance " shirt I feel much cooler (even in a dark blue one) and sweat far less. I also drink less water in those shirts. Example: http://www.mec.ca/product/5032-035/mec-rhythm-long-sleeve-womens - I have no affiliation, I own three of that shirt though.
A long sleeved loose shirt, even if it's not a special cooling shirt, may well be cooler than bare skin and will protect against sunburn. You may also be glad of it when you go inside and the air conditioning is on stun.