I feel like you can do a modified version of bike commuting no problem.
In addition to the other good advice already given:
Doublecheck your route. You may find a more pleasant or even shorter route. For example it's inconvenient (and kind of rude) to take shortcuts through a residential area in a car, but not necessarily by bike.
Are you sure sweating will be such a problem in the morning? Sometimes when the big giant burning thing hasn't been in the sky for as long, it's cooler. And you're leaving 45 minutes earlier than you normally would. You might even try coming in to work an hour early to get more done and to beat the heat.
If you do bring extra clothes, you can drive in Monday morning with a week's worth, then you don't have to carry as much on the bike.
Don't forget to bring extra snacks. Particularly when you first start, the ride will make you hungry.
Definitely think about your options with biking some days and driving others and think about juggling whether the car or bike stays at work. Since you have a long ride and it takes a little while to build up endurance, it's great to have options like biking in in the morning, taking the bus home at night, taking the bus in the next morning, riding the bike home that night, etc. So you don't burn out biking 24 miles a day right away. Along the same lines, I would give yourself plenty of time to bike in the mornings. Nothing ruins a nice ride like having to push yourself to go faster, plus that will help with sweating (eventually you'll get competitive with yourself about how fast you can make the trip and that will make you a stronger rider, but that's different)
Personally I would stick to the cruiser at first. That way you're not out any money just for trying and you get a feel for what you would really want in a bike. Of if you already know what you want, for a good deal to come up on Craigslist.
Good luck!