Hi Toddy
The problem you will have is most of the heat reflective material readily available ie emergency blankets etc are highly flammable. Anything that has any form of nomex fire proof material or kevlar backing are likely to be very expensive.
I use one of the open fronted type fisherman shelters at archery comps and they would not take to kindly to stray sparks from open fires. I have used small gas stoves carefully positioned, but I do not think this is what you had in mind. If you adapted one with some proofed cotton it might not be as flammable, but would certainly weigh more. At the summer Bushmoot, the aluminium foil type material was being discussed a lot by Mors, and its possible use in emergency shelters for civil emergencies, mainly as a roof material to reflect heat back into the shelter. The only problem I could see in a small shelter with a fire in front of you, you might end up too warm, and feel like a xmas turkey.
Chas