Temp Sensor - Incoherent values when unplug from USB


I have a temp sensor LM35 with provide me with temperatur properly (and similar to an external device). Everything seems to works fine up to the moment where I unplugged the USB cable. At that time the Arduino (Uno and also Mega2560) provide strange values

For example : the "right" temperatur is 21 or 22 degre. This value is properly detected and received when the 2 cables are plugged (the power supply and the usb connector)
As soon as I unplug one of these 2 cables, the behavior is the same, the data displayed are really strange, such 35° and something up to 40 degre.

Do you have one idea and / or a solution ?
Thanks in advance

how is the MEGA powered?
what is connected to the device?
can you post a schema?

have you measured if the 5V does not drop?