After researching other open-source growth chambers, I concluded that most of them do not use proper insulation. The disadvantage of that is, that the heat transfer from inside the chamber to the atmosphere would be relatively high and thus maintaining a constant temperature would be difficult.

On this basis an insulating material had to be used and fitted inside the walls, base and ceiling of the chamber. Polyurethane foam was chosen because of its wide commercial use, has a high r-value per cm and can be easily cut using sharp tools. 

Another important aspect is the reflective properties of the inner side of the walls. Having a high reflective index would mean that the distribution of radiation to the plant would be greater, and therefore the plants would have a better environment to grow in. 

Because polyurethane can not be used for this purpose another material had to be chosen; white acrylic. It has the suitable reflective characteristics as well as it is easy to shape using laser cutters.

Finally, for the outer side of the wall, polyurethane alone would be weak and vulnerable against the outer environment and therefore plywood would be used as the an outer shell because of its rigidity, low cost and ease to be shaped. 

In conclusion, there would be three layers in the walls, base and ceiling of the chamber:

1.  Inner layer: white acrylic, 3 mm 
2. Middle layer: polyurethane, 25 mm
3. Outer layer: plywood, 6 mm