Pirelli’s release below doesn’t get into much detail about the differences between the TD and the Supercorsa’s other compounds, but in general, having a broader range of operating temperatures helps riders who ride to and from the track.
Begin press release:

Pirelli Tire North America is excited to announce the availability of an all-new track day-specific motorcycle compound of the DIABLO Supercorsa family. Pirelli?s latest offering, as well as all DIABLO Supercorsa products, is DOT approved and geared towards delivering motorcyclists the ultimate combination of racetrack performance and durability and will be available in a total of seven sizes.
?We?re proud to offer this DIABLO Supercorsa special compound for track day use as it?s designed to keep up with the performance and technology of today?s sport bikes,? said Oscar Solis, road race manager, Pirelli.  ?The solution is incredibly versatile, giving riders the ability to cover both street and racetrack in a DOT legal package. It provides riders the opportunity to competitively log laps at their local track day and hop on the street to ride a scenic canyon route back home.? These special tires feature a unique ?TD? tire sticker, creating a distinct look on the sidewall in comparison to other tires in the Pirelli DIABLO Supercorsa lineup. Trackside vendors will offer the tire for sale across the country and at upcoming events including March 29-31 at Chuckwalla and MSR-Houston, April 12-14 at CMP and ...