For better results it more important to use thermal paste in between aluminium rectangle pipe and peltier. With this aluminium will keep the peltier at room temperature.
Your aluminium rectangle pipe should be like a heat sink. This will also keep the peltier at room temperature all the time.
If you have Strawhat 8mm 0.25W LED its ok. Actually I find 1W special LED has better results not every 1W LED. If you find this 1W LED then take other strawhat LED is ok. Every 1W LED has a yellow colour dot in its centre. Always take that 1W LED that has very small yellow colour dot. You can see in the picture yellow dot. The LEDs having mark are ok and having cross are not ok.