If you are serious about commuting, you should get a better bike for commuting on. The Trek Domaine is a fine bike for racing, but for commuting you want something that you can easily hang stuff on like bags, lights etc.
I have an almost identical situation to you - I have an 8 mile commute to work, at work we have a gym, with showers etc, and a room where we can store bikes, which has tools, air etc. I ride in to work hard enough to work up a sweat, and then shower and get dressed at work. I park the bike in the storage room. There are power outlets in the bike storage room to recharge batteries etc. After work, I ride home slowly enough to be able get home without being too hot and sweaty.
My bike (which cost about 50% more than the Trek Domaine 5.2) has a rack, fenders, lights, beefy tires (one flat in the past 13000 miles). I have another bike that is for fun fast rides, but I don't commute on it.