Reduce time to stable value in PID
Before you mess with the system make sure it's safe before you start playing with gains. If it overshoots it could have disastrous consequences if the system isn't bounded (either physically or with the controller output).

Try turning up your gain, realize that if you do so you will sacrifice stability. If you need to, then increase the integral term. Rarely do you need to use integral, but a small amount can help reduce noise in a first or second order system. 

I'll bet that your system could benefit from some integral.

Below shows a graph of a system that shows an example of what different gains do. 



There are also a few methods like Ziegler-Nichols that can be used to efficiently tune PIDs.

You may also be limited by control authority, meaning if your system hits the limits or rails (like if the thermal system is warming up and your PID is output 100%, or if your heater or peltier is at max power) then you will need to increase the control authority (or heater power).