You can also use an op amp configured as a differential amplifier. A 2.9V reference.Thanks Ron for the details
Maybe around 20 years ago I've seen one literally melting on a protoboard. Brave, it worked until the last moment.
As shown the op amp will output 0 to 4.0v with your input range to 3.7V max. Then set internal voltage ref to 4.096. You get almost the whole range of ADC at 1mV/bit on 12 bit ADC.
Be sure to use an op amp with output to ground.