If the sensor is getting hot, then it could be fake or connected wrong..
Post a picture of the setup.
The TMP36 is an analogue sensor, so temp readout highly depends on Vref and the supply of the Arduino.You must switch to one of the internal reference voltages of the Arduino to make this sensor less dependent on (USB) supply voltage.
If you don't have analogReference(INTERNAL in setup(), then expect instability.
It could be much easier to use a digital sensor, like the DS18B20, than to make this analogue sensor work reliably.
Leo..
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