The question is if I can manage the timing correctly.
I think this would be a bridge too far.
All I really need from the temp sensor on the remote end, is a high pin when the temperature is over a specified trigger value.
The DS1821 can function as a standalone thermostat with user-programmable trip-points or as 8-bit temperature sensor with a 1-Wire® digital interface. The thermostat trip-points are stored in nonvolatile memory, so DS1821 units can be programmed prior to system insertion for true standalone operation. The DS1821 has an operating temperature range of -55°C to +125°C and is accurate to ±1°C over a range of 0°C to +85°C. Communication with the DS1821 is accomplished through the open-drain DQ pin; this pin also serves as the thermostat output.