  r-mode astroseismology provides a unique way to study the internal
composition of compact stars. Due to their precise timing, recycled millisecond
radio pulsars present a particularly promising class of sources. Although their
thermal properties are still poorly constrained, X-ray data is very useful for
astroseismology since r-modes could strongly heat a star. Using known and new
upper bounds on the temperatures and luminosities of several non-accreting
millisecond radio pulsars we derive bounds on the r-mode amplitude as low as
$\alpha\lesssim10^{-8}$ and discuss the impact on scenarios for their internal
composition.
