Infact you are not using STDERR at all and in the case of a use of warn a newline is added anyway. From the docs:

Prints the value of LIST to STDERR. If the last element of LIST does n
+ot end in a newline, it appends the same file/line number text as die
+ does.
[download]

In case of need of a granular control over buffer behaviour you can use the autoflush method from IO::Handle that is the base class for all other IO handle classes.

In your example you just need to put $|++; after use strict; use warnings; lines.

L*