TMP36 temperature sensor reads for a while and then jumps up 30 degrees C

I'm new to arduino and working through the 15 projects in the starter kit.

Project three uses the TMP36 sensor.
It works fine (reads 15C) until I put my fingers on the sensor to increase the temperature reading.
Then it jumps up to temperatures in the 40 - 50C range and stays there for a considerable amount of time after I remove my fingers.

I modified the program to take 20 sample readings and then to use the mean of the 20 to give a reading. It didn't help.

Anyone had this experience and can explain why it happens?

First of all: TMP36 is not very accurate (+/- 3°C).

Then there might be an error in your sketch but you didn't show us your code. You also didn't show us your hardware setup (wiring diagram).

There is no "The starter kit", there dozens of starter kits available, so any reference to a project number or the like don't show us what you've done.