Derivative using a PID Loop

I am using a GE90/70 PLC.
Is there a way to use a PID loop to take the derivative of a temperature. If the temperature increase is more than 31.6 F per minute then the ouput pid would increase?

Wow, you've got some unique ideas about using PID!

When you say "take the derivative of a temperature", do you mean calculating the rate of change of the temperature with time (dT/dt)? If so, it's far easier to just do the arithmetic than try to extract the derivative from the PID equation.

Set up a self-resetting timer or a timed interrupt at any convenient time increment. Calculate the difference between the current temperature value and the stored value from the last time you did the calculation. Divide that difference by the time increment to get the rate of change, and copy the current temperature value to the storage location.

analog PID work with very small deviation.
so if you want something if over a border then you will have to make your own program.
If you want to look for sharp peaks in small time you can use two samples and the time in between. calculate minuteraise by 60000/looptime*deviation.
if you want to have average you will have to take a lot of samples and check every minute if average is climbing to much.