from Temperature T1 to T2 in a fixed time

Hi All,
It must take 2 hours to reach a temperature of 55°C starting from an ambient temperature of 22°C.
I have to stay at 55°C for 20 minutes.
It must take 1 hour to reach a temperature of 65°C starting from an ambient temperature of 55°C.
I have to stay at 65°C for 20 minutes.

To stay at a temperature
and moving to another PID can be a solution.

But when I have to go from 22°C to 55°C in a fixed time of 2 hours, is the PID still fine?
Many thanks.

To use PID to change temperature slowly, change the setpoint by a small amount, in many time steps over the total period.