Here is a first pass at a circuit. It is very simple because all of the real work is done in firmware inside the PIC.
RA5 is configured as an A/D input. This plus a look-up table in firmware is how all temperatures are captured, stored, compared, etc.
RA3 is the switch input. The PIC can either poll this input or the input can be configured to pull a hardware interrupt. The switch is debounced in firmware.
RA0, RA1, and RA2 drive the three LEDs. Because only one LED is lit at any time, only one current limiting resistor is needed.
C1 and C2 are power supply decoupling caps for U1 and U2. These should be as close as possible to the device power pins.
If you are asking about a circuit external to the PIC that can sample a voltage that is proportional to the current temperature, and then compare that voltage to the sensor output as the temperature changes, that is a very different problem.
It can be done with a sample-and-hold circuit (or IC) and a pair of comparators, but it takes a very high quality capacitor and high-impedance electronics. You don't say how long the circuit has to hold the reference temperature, but the longer the time, the more expensive the cap. Pre- and post- WW II, this was the way these things were done, so there is nothing new there. But it will be much larger, and more complex and expensive than a PIC solution - IF - you have the hardware, software, and coding skills.
UPDATE:
First, as hack says, consider using a thermistor instead of a temperature-sensing IC. In the coding, the only difference is a different set of values in the lookup table. Some thermistors are accurate to 0.1 degree C without calibration.
Also, you don't need a separate input pin for the switch. If the switch is directly the (thermistor) temperature sensor, the uC can see when that analog input goes to 0 V and use the most recent non-zero reading as the new setpoint for the comparisons. This eliminates one resistor and reduces the total number of I/O's to 4, so you can use an even cheaper uC.
sensor
withcontroller
... the sensor detects temperature ... the controller receives data from the sensor ... the controller lights LEDs \$\endgroup\$