STM32F103 temperature sensor calibration addresses
The STM32Cube library for your part includes one or two helper macros for calculating the temperature from an ADC reading of the internal temperature sensor.  The User Manual for the HAL and Low-layer (LL) Drivers describes these macros.  The implementation differs from one STM32 family to another so make sure you get the information for your particular part.  Even if you're not going to use the STM32Cube library you can still refer to the source code for an example of how the temperature macros are implemented.

The two macros are __LL_ADC_CALC_TEMPERATURE and __LL_ADC_CALC_TEMPERATURE_TYP_PARAMS.

Some STM32 parts have temperature calibration values that are measured during manufacturing of the device and programmed into ROM.  These parts use the __LL_ADC_CALC_TEMPERATURE macro.  This macro uses the ROM calibration values to improve the accuracy of the temperature measurement.

Other STM32 parts do not have temperature calibration values in ROM.  These parts use the __LL_ADC_CALC_TEMPERATURE_TYP_PARAMS macro.  This macro uses the "typical" values for Avg_Slope and V25 taken from the device datasheet.

I believe the STM32F1 family does not have temperature calibration values in ROM so you would use __LL_ADC_CALC_TEMPERATURE_TYP_PARAMS with the typical parameters from the device datasheet.

If you want to improve the temperature readings you could calibrate each of your units during production and store the custom calibration values for Avg_Slope and V25 in ROM.  Then substitute your custom calibration values for the typical values from the datasheet.