A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated. If it is heated uniformly to raise its temperature slightly then..

When the rod is uniformly heated, the length of it increases in both directions across the center of rod keeping the mass of rod constant.
Hence the moment of inertia of the rod about the axis of rotation, $\mathrm{I}=\frac{{\mathrm{ML}}^2}{12}$ increases.
Since angular momentum of the system must be conserved, Iω is conserved. Increase in I implies decrease in ω.