As far as I know, there are no specific eukaryotic or prokaryotic factors that aid in RNA folding other than cellular environment (salt and ion concentrations, dissolved molecules, etc). Are there any factors to consider when introducing eukaryotic RNA in prokaryotes? Is it possible to predict the proper shape and folding upon introduction to a prokaryotic cell?
As you have mentioned ions and temperature affect RNA structure. There are also different types of RNA structures and their dependence on ions are different. Mg2+, as Mad Scientist mentioned, stabilizes duplexes; so do monovalent cations like K+ and Na+. However, Mg2+ favors duplex over quadruplex if the same RNA can adopt both these conformations. Dependence on temperature is a trivial case.
Ions and temperature should be more or less same for prokaryotes and eukaryotes unless we are talking about extremophiles.
Apart from these factors I can think of two other factors that can cause difference in RNA structure between prokaryotes and eukaryotes:
It has been shown that TMAO (Trimethylamine N-oxide) stabilizes RNA secondary structures. The metabolism of TMAO is different in prokaryotes and eukaryotes.
From this paper:
I cannot ascertain that this will affect RNA folding but is possible.
This is something that you can be certain about. Some RNAs require protein counterparts to adopt a functionally capable structure. In the absence of the protein they may not form the relevant structure. So if an RNA needs Hfq then you have to express it in the eukaryotic system where you want to use the RNA (and converse).