Why did the manufacturer do this crazy thing? Well IMHO, they either bought in the main controller's code or commissioned it in-house to work with a digital sensor, then either the digital sensor was discontinued, or they found it was too expensive or it had some other problem (e.g. transients killing it or the main MCU) and they had to patch up the design without the help of the programmer who coded the main MCU's firmware. Using a slave MCU as an ADC is a valid strategy, but is usually only seen when you need multiple ADC channels electrically *ISOLATED* from the main MCU dirt cheap, as you only need a single optocoupler for a one-way serial link.
Maybe its time to buy a Salae 'Logic 8' clone, which are dirt cheap and readily available on Ebay, Amazon and the usual far east marketplaces, to use with the FOSS
Sigrok software. Here's Sparkfun's
tutorial. If you post dumps in Sigrok format there are plenty of users here who can help you decode them.
If you are very lucky, we may be able to identify the protocol and match it to a digital temperature sensor IC that's still available N.O.S., in which case you may be able to replace the thermistor with a sensor IC, possibly with an extra Vcc wire to it, rip out the PIC and jumper pins 6 & 7 of its footprint.
Once you've got enough good data to make a fair guess at the protocol, you could set up an Arduino and code a sketch to decode and log the data and also the temperature from an independent probe on the water bath, and fill the bath with boiling water then log as it cools to ambient. That will give you the temperature vs output data relationship, which you'll need to create code for a replacement PIC.
Nearly *ALL* Microchip's 8 pin PICs have the same pinout. If coding up a replacement, it would make sense to use one with lots of memory and a 4x PLL to boost its clock speed, so you can get away with using the XC8 C compiler in FREE mode (which disables many optimizations so generates slow and bloated code) rather than having to wrangle with PIC assembly language.
To answer your pin 4 query: on 8 pin PICs, its dual function, used to enter programming mode and also as an active low Reset pin. It may also be an input only GPIO pin so you may well see it called out in datasheets as \$\overline{MCLR}/V_{PP}/GP3\$ (i.e.
/MCLR/V
PP/GP3 if you are having Mathjax rendering problems). On older PICs, taking this pin up to Vpp, (>>Vdd) entered programming mode, taking it down to logic '0' reset the PIC and you needed to keep it at logic '1' (<=Vdd) for the PIC to run. Newer enhanced midrange PICs got rid of the high voltage Vpp, as they use a different protocol for entering programming mode, but unless external /MCLR is disabled in their CONFIG bits so the pin can be used as an input, still need it at logic '1' to run code.
TLDR: Its a *LOT* of work, not commercially viable to repair, but would be a great learning project if you want to get into sensors, comms protocols and small MCUs.