Electrical – 2 voltage measurements same circuit Arduino Uno

You can neither correct it in software, nor use a diode or resistor to drop the voltage if you don't know the cause, or the error function. You get 44° instead of 22°. What would you do to solve this? Divide by 2? Would a reading running on USB of 15° also result in 30° when running on the batteries? A diode would be a bad solution in any case.

My first reaction was that the batteries would give a too high voltage. The first line of the datasheet says 2.7V to 5.5V operation. Now if those were Alkaline batteries you would have 6V, that's outside specifications, and then anything can happen. Always make sure you're within specs before you start looking at other things.
But you say they're rechargeable, that's probably NiMH, at 1.2V per cell that would give you 4.8V, almost the same as the USB's 5V. That can't explain it.

I realize it will be a simple schematic, but still: post it here. We'll need to have a look at every possibility. In the mean time, measure the batteries' voltage and report back.

The connection to the Arduino will be thus:

^{simulate this circuit – Schematic created using CircuitLab}

You can use either an analog or a digital input pin on the Arduino for reading from the device. The specific values of the resistor and capacitor are not critical, so long as the resistor does not limit supply current below around 5 mA, which the datasheet specifies as the Absolute Maximum the component could ever need. This means resistor values of up to 1 kOhm will be fine.

The R and C in the datasheet application circuit example are there to eliminate any high frequency noise in the supply circuit. With 100 Ohms and 4.7 microFarad, this filter has a cutoff frequency of around 340 Hertz, so it will smooth out power supply noise over that frequency.

You could use 220 Ohms and 2.2 uF for a similar effect, filtering out any power supply noise above around 330 Hz. ... Or any such combination of R and C. No, don't leave out the capacitor, else the power filtering purpose is not fulfilled.

Neither the resistor nor the capacitor really have any relationship to the voltage the TSOP part is powered with - other than that the capacitor needs to be rated to operate at well above such supply voltage. Since the 2.2 or 4.7 uF capacitor is most likely to be electrolytic, ensure that the capacitor is rated for 10 Volts, and is connected with the correct polarity, i.e. negative pin connected to GND, positive to Vcc through the resistor.

Note that the datasheet states Supply Voltage (V_S) of 4.5 to 5.5 V. While the TSOP series does operate at 3.3 Volts from personal experience, this is below the rated supply range, hence functionality is not guaranteed, and may occasionally fail.