Hi Cristian, My suggestion is to get your vehicle checked and diagnosed because water can do internal damage to different vehicle components including but not limited to the transmission and/or engine. It's best to avoid puddles when ever possible because they can turn out to be deeper than they first appear to be. Good Luck.
〉 Answered on Oct 5th, 2013 by Maryann Croce, Owner at Croce’s Transmission Specialists
If the car was just smoking for a few minutes after going through the puddle, then it is probably just from the water burning off. If is continuing to smoke, then you should take the car to a repair shop to get looked at. Water might have gotten in when water should not be.
〉 Answered on Oct 5th, 2013 by Helaine Kurot, Owner/Technician at 360 Automotive
While it's possible that it got into your crank case. It could just be drying off from the heat of the engine. If it persists, see a mechanic.
〉 Answered on Oct 5th, 2013 by Barb Petrey, President - DBK Enterprises Inc at Jiffy Lube
Typically going through a small puddle won't cause internal damage you were likely seeing stream from your hot exaust system.