I have a completely open loft (no wooden beams etc across the space)
with concrete floor and no insulation or cladding (you can see the
underside of the tiles etc...)

I'd like to use this space as an office but the temperature varies a lot
with no insulation etc.

What's the cheapest way to sort this out. I have been told that
cardboard makes a reasonable choice, but I guess it doesn't look good
and is certainly a fire risk. I don't want to spend much money as the
house isn't mine...

Would some insulation material and a load of plasterboard do the job?

I'm in a similar situation (except for the fact that I do own the loft, it's
not made of concrete, it is insulated and it does have wooden beams crossing
the space) and was planning on just using the foil loft insulation roll
stuff from ScrewFix @ £5.56 per square metre. I have no idea whether this
is a good idea or not but I presume you can just board on top of it,
although plasterboarding a loft you don't actually own would seem a bit
excessive in my book! How would you actually get the boards up there
(without cutting them) for a start?

Andy