I have a SOL Thermal bivvy which is basically a fully waterproof and non-breathable emergency shelter.
Would placing this on, under or around my sleeping pad do anything to increase its warmth?

What sleeping pad do you have?

If it's an inflatable mattress the SOL may add a bit if the mattress is placed inside it since the reflective lining of the SOL could reflect some radiant heat. I wouldn't imagine that it would add much either on or under the mattress though.
Would keep your mattress cleaner....

I'd not want to spend a night in the SOL BB. Why not put an ad out for 'bivy needed' and see what folks come up with. Only one thing worse than having to sleep inside a SOL (yes, I've tried the rather unpleasant exp) and that's trying to do it in the winter.

Besides, if you put the SOL directly onto ground and not your mat then you'll have the added pleasure of helping it become at least a bit breathable (a tiny fraction of a percentage) and less waterproof

Enjoy.

Well, I may have misunderstood!
I thought you meant increase the warmth of the sleeping mat rather than increase the warmth of the bivvy
If you mean increase the heat of the bivvy then on the mat would be best with mat underneath; that way you get the full benefit of the reflective lining reflecting your body heat inside the bag.

I'd stick your mat in it. At a guess, under won't stop an uninsulated mat losing heat, on won't double the insulation effect but mat in will help a bit and also keep your mat clean.

Sol escape bivvy in your sleeping bag is my go to method of increasimg temperature of a bag
No idea what.the effect is of what you ask but would place it between me and mat personally ( possibly inside out )

Ah OK The idea was to place the mat which has around and R2 rating inside the SOL thermal bivy- I would put a lightweight CCF mat underneath the pad and then synthetic bag and down quilt inside a Hunka bivy.