A sheet soaked in cold water might work - it all depends on exactly how cold you want something to be, how large it is, and the context.
You might need a slab of refrigerated steel, or a gentle waterfall of cold gas from either liquid nitrogen or dry ice to act as a cooling film. It's rather hard to say.
Feel free to describe what it is that you are photographing, the scale, and the temperatures needed.
Thermal imaging cameras might have different temperature range determined based on the infrared wave length emitted from the object. It’s better to use a background which is In thermal equilibrium with the environment because the object temperature would be distinguished based on this reference value. Any background hotter or colder than the object itself is a problem because that it might just be over or under the limit of camera calibration. I use a thick black paper sheet as a background for thermal imaging with FLIR x6540sc model and it works well.
Judging from the parameters of your question, thermal conduction is not your problem. Rather thermal transmission and reflection are your issue. - specifically in the infra-red range.
The Jodrell Bank astrophysical research centre in the UK has a clever display in which they demonstrate the use of commonly available plastic films to control both reflection and transmission of IR. Obviously this is a major issue to them as cutting out Earth based IR makes deep space observation so much easier. They use thermal cameras and frames containing such materials to show that simple materials can defeat heat leakage in unexpected ways.
I was playing with their demonstration only last night a (Feb 7th) and it was quite obvious that materials that are reflective in visible light may not reflect IR at all.
I would suggest you experiment with easily obtained materials such as waste bin liners, packaging materials and the like.
As Subasish suggests, black paper or card may be your best answer.