AC/heater temperature control

Entire AC system recently rebuilt and works fine when it works.
I set the temperature at sixty degrees and turn the AC on.
Sometimes it blows cold and some times it does not.
It is very hot now, near one hundred degrees, in the St. Louis, MO area and the system will not blow cold.
I have been told my "HVAC controller" under the dashboard needs to be replaced? Is this correct?