How would the "pros" bike this commute? I've been putting up some pounds and have a bike gathering dust at home =D

I normally commute by bus or carpool, but would like an opinion from some more seasoned bikers on how you'd tackle this commute http://goo.gl/maps/0ts21

My excuses are:


It's scary, for me at least, because the destination is at some big highway with trucks and everything racing at +80 km/h.
Bike lanes down here in .mx are not even a concept in most parts of the country.
No place to shower at the destination and the job is white collar.
Crazy hot weather, up to 40°C and above at times.


So the questions are:


Is this doable?
If so, how should a noob tackle it?


Thanks for reading and do share any insight you might have.
I took a pretty quick look at the map, but I'm going to make a kind of general suggestion: If this is a trip that you're only used to traveling by motor vehicle, you might fall into the trap of thinking that the route you're used to is the only route available. Bikes can go lots of places that cars can't, and lots of places that cars just as frequently don't. 

If you're just starting out, I would suggest avoiding the highway; it will just be really un-fun and discouraging. What I might suggest is that you start taking your bike out in the evenings, and start looking for other possible routes. You could even do some of this on your drive home. 

The heat and the lack of shower space is something that really depends on your comfort. You should be able to avoid the heat of the day, and you won't be out long enough to really worry about dehydration, but you might want to at least change your shirt when you get to the office, and have a towel or something to wipe yourself down.