In order to calculate the temperature ranges in the MAX20353, you need to understand the Thermistor circuit, which is a simple resistor divider network, where TPU pin is connected internally to the VDIG =1.8V and the THM pin is connected to an 8bit ADC that reads the output of the resistor divider network.
Depending on the NTC thermistor you use, there might be slightly different performance, but usually the 10kΩ NTC is equivalent to 10kΩ at room temperature (25 °C) NTC R/T Calculation 5.0 (tdk.com) or NTC RT Calculation Tool | Thermistors | Vishay. Check the calculator provided by the manufacturer for the part you implement in your design.
Now you will think back to the basic resistor divider, you can use this handy tool from Digikey Voltage Divider Conversion Calculator | DigiKey.
With an Input voltage of VDIG = 1.8V, it means that the output voltage will be 0.9V at 25 °C (R1 is the fix 10kΩ resistor, and R2 is the NTC 10kΩ thermistor)
For example, if you want to enter 0°C for Cold register, then get the NTC resistor value at that temperature from the manufacturer. For the one used in this example, the nominal resistance at this temperature is 35563 Ω. With the resistor divider calculator, you should get 1.4049V, and that is what you need to enter in the cold setting.
Since the register is an 8-bit value and the full-scale voltage is 1.8V, then you will get the LSB of the register by the following equation:
LSB = 1.8/2^8 = 1.8/256 = 0.00703 V
The value you need to enter in the register is the equivalent of 1.4049V.
Therefore, the register value = 1.4049V/LSB = 1.4049/0.00703 = 199.84 in decimal
If you round up to the nearest value 200, the 8-bit hex value will be 0xC8 in APDataOUT0 register to transfer when the APCmdOut (0x16) is called.
You will need to perform the same for all the other temperatures limits the design requires to set for cool, warm and hot.