You can certainly go down the coast as you make your way down to Rome! Just remember, it is the the Tyrehhnian sea, not an ocean, so it will definitely be more calm and warm waters ;-)
I suggest from Florence to head down diagonally toward the coast, making your way to Volterra and from there west toward the coast - you get to enjoy driving through the Tuscan countryside and great views!
Drive through Bibbona down to
Bolgheri and to
Castagneto Carducci, this is wine country.
Try to arrive at
Campiglia Marittima by evening... this area is known as
the Etruscan coast. Campiglia is magnificently medieval with remains of a fortress at the very top. We also enjoyed
Suvereto, also medieval... if you head toward the coast and beaches here, I suggest the
gulf of Baratti (Populonia just above is an Etruscan necropolis but not sure how much time you will have here by then).
The next day you can keep moving south along the Via Aurelia past Grosseto ( a quick stop downtown to see the cathedral and Medici fortress is recommended) then on to Manciano if you want to go to
Saturnia. I suggest you spend the night in
Pitigliano, it is a wonderful charming town carved into what is called "tufo" rock in Italian (the first pic you see at the top here:
http://www.discovertuscany.com/maremma/what-to-do/). You should explore Pitigliano for sure... there are 2 more "tufo" towns in the area, Sorano and Sovana, but again, see how much time you have by then.
The hot springs are warm, but it is water... so even in summer it is nice to get in and out of it! And we aren't guaranteed super hot summers anymore, last summer was quite a wet one and thus very nice.
From there continue south back on the Aurelia, it is the fastest road.
Everywhere you'll go you'll get a chance to do lots of wine tastings - always go the "local" wine. Near Campiglia you have
Bolgheri, in Saturnia are you have
Morellino di Scansano, both red wines. You can always get other Tuscan wines anywhere in Tuscany, but these areas have wines that are less known abroad so will get you a chance to give your tastings buds the chance to try something slightly different ;-)