This has me confused.

Temperature can be used to refer to how fast the atoms are jiggling (kinetic or phonon temperature) or to how messy, disordered (opposite of ordered) a system is.

Time dilation is a relativistic effect where time appears to go slower when you are looking at something that has a very high speed (near light speed) compared to you (relative velocity). Can also happen with mass because gravity is acceleration, thus related to velocity.

If the atoms are jiggling slower, relative velocities only shrink, so you'd expect to see less relativistic effect. I am not aware of any relativistic effects due to thermal motion in normal conditions (room temp, atmospheric pressure), so I don't know how they'd appear when relative velocities only decrease.

I am really interested where you got this temperature - time dilation link from. Can't seem to crack it.