Since my transition area is longer than the length of my T-molding, I need to place a second T-molding. Is is proper to merely allow the two T-molds to abut each other or should I cut them like you would do with baseboards? Thanks in advance.

I ususally join the seam at a 22 1/2 degree angle, matching up grain and shade close as possible, and choosing the best location.

Thanks for responding. Since I'm a novice, this follow-up Q may sound a bit dumb: What tool is the correct one to perform a 22.5 degree cut: table saw or miter saw?

I use a mitre saw for a more accurate, cleaner cut. Mitre saws will lock in at the 22 1/2 degree mark. I prefer that angle over a 45 due to the sharpness of the point on a 45. I think the 45 is tougher to hide, plus the sharp point is bound to catching.
The cut can be made on a table saw as well, just easier to make on a mitre.