The biggest issue is probably your front derailleur. At a minimum you'll want to slide it down your seat tube to position it 1-3 mm above the large ring's teeth when the outer plate is directly overhead. Less likely, the front derailleur's arc isn't wide enough to accommodate the slight increase in distance to the outer ring on a triple crank.

Shimano has technical documents for their equipment going back years that covers installation, adjustment, and specifications. Other manufacturers are the same. BB width is more defined by the frame than the crank. Read up on chainline. Your swap is likely to shift your effective chainline to the right a few mm, since shimano uses the center of a crankset to determine chainline. That's over the middle ring in a triple, and halfway between the two rings on a double. The threads about chainline should give you an idea about what to look for and expect.