There is no simple answer to this.
A simple formula for the capillary rise , h is
h = 2TcosL / r p g
T is the surface tension, L is the contact angle, r is the tube radius p the liquid density and g the gravitational acceleration.
Now both the surface tension and the density decrease with increasing temperature.
The tube radius will increase. the other quantities are unaffected.
So it depends upon the relative changes for the liquid concerned.
In general the surface tension will win out and the upstanding column will fall slightly.
Somewhere near the liquids 'critical temperature' the surface tension will reduce to zero and the rise will disappear altogether.
