A furnace sounds like a hot place to do computer work. Why not do FEA at your desk?
Greg's process is the real world, i.e. FEA is the big hammer you use after trying other, cheaper and easier, tools first (build and test, do some hand calcs, try again, if it still breaks look at FEA...)
Step 5 of Greg's process is "iterate 2 and 3 along with building and testing until a solution is found or you run out of money or time or both".
There are some on-line free FEA solvers (e.g. SimScale) that will accept .step files from Inventor; it has some limitations in the types of FEA that can be done. The InventorPro FEA solver is Ansys based, and works acceptably though is also limited in the types of FEA that you can conduct. The full Ansys solver package is spendy, but has a very good reputation, and can do quite a variety of stuff. All FEA solvers have a fairly steep learning curve if you are new to the process. Careers have been made doing FEA analysis.
My initial question is what you want type of analysis you want to do with FEA? FEA is tool that can analyze a lot of different things, strength, temperature and so on.