I claim the ornamental design for an air conditioned running cap, as shown and described.
FIG. 1 is a front perspective view of the running cap.
FIG. 2 is a rear perspective view thereof.
FIG. 3 is a front view thereof.
FIG. 4 is a rear view thereof.
FIG. 5 is a right side elevation view of the running cap.
FIG. 6 is a left side elevation view thereof.
FIG. 7 is a top plan view of the running cap; and,
FIG. 8 is a bottom view thereof.
The dash dot dash broken line defines a boundary line to the claimed design and forms no part of the claimed design. The dash dash broken lines depict portions of the air conditioned running cap that form no part of the claimed design.