Microchip AN1333 provides some detail on the Internal Temperature Module -
http://ww1.microchip.com/downloads/en/AppNotes/01333A.pdf
Figure 4 gives the clearest idea of temperature versus ADC reading, though ADC is 8-bit there and the PICAXE uses 10-bit. The references used I believe are the power rails.
Figure 5 shows how the temperatures can be offset vertically depending on chip, and Figures 6 and 7 show how the slope can vary, mostly with power supply voltage.
The formulas in the manual are a rough match for a typical vertical offset and slope that was found in the samples we tested to convert ADC readings to degree C and is primarily for positive temperatures.
To get the most accurate conversion it is best to take a RAW_H or RAW_L reading and apply an equation based on an actual calibration of the chip. To handle negatives it's probably easiest to offset temperatures, for example, so -40C reads as 0, 0C reads as 40, 100C reads as 140 after the appropriate equation has been applied.
Alternatively, work through the temperature split points you are looking for, make a note of the raw readings, then use those as constants to compare against to determine band. This can avoid accuracy issues in the equations.