If I have 36,235.97 BTC, would I shorten that by writing that I have 36.2k BTC or would I write 36.2 kBTC?
It seems that latter is proper for SI units, while the former is used more often for money, at least in the U.S.
I would write 36.2K BTC.
On the other hand, if I had 0.0362 BTC, I would write 36.2 mBTC.
As BTC is written on the right side of the amount, it suggests being more like a science quantity, rather than a currency, which usually have their signs on the left side. So I'd argue that if you want to write 36,235.97 BTC, you should do it like 36.2 kBTC, but if you wanted to write BTC36,235.97, you'd write BTC36.2k. I haven't seen the latter version used, so probably the first one would be preferred, but then again, nobody would notice anyway...
Definitely 36.2k BTC.
As you noticed, it's what is most used for money anyway.
And, for the record, I'd never short lesser units as @Meni suggested, because it would only cause confusion: it's not a SI unit we are talking about, it's money, and money uses different conventions.