Delay decreases as u decrease ur th voltage as switching time decreases and abt the mobility it will increase till a certain point as temp increases It has to do with the work function i guess just check.
For example, when temperature increase, the VT will reduce, then it can be turned on easier, so the delay will redcue, then frequency will be improved.
But it is not so simple, because when temperature increase, Ron of MOS will increase, so the current for charge the parasitic capacitor will reduce, then the next stage will be slow. So the frequency will be reduced.
So, when the temperature increase, the delay and frequency will increase in some temperature range, and will reduce in other temperature range.
But the Vth will reduce with the temperture in the whole range.
This is all detemined by the physics of semiconductor.