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You are correct… care must always be taken when working with a load bearing wall. However, most load bearing walls are purposely over-engineered, meaning that they are built to take loads way beyond what they will probably ever have to bear. That said, minor changes to them can be made without compromising safety provided that the change is done in such a way that the strength is returned to the wall. For example, to install a window into a load bearing exterior wall you must install additional vertical supports along the edges of the window to support a strong horizontal support, or header. The header transfers the weight from above to the outer edges of the window frame.
This situation is probably similar to yours. If you remove this wall, you will probably have to install a header or beam across the top of the ceiling to restore the wall's strength. The two questions I can't answer are 1) whether you need to install temporary supports or "jacks" on the ceiling to hold it up while you install the beam… also known as "shoring"… and 2) the exact design and load carrying ability of the new beam. If the wall you are taking down has other support such as adjacent walls, you may not need any shoring during construction". In many homes, some so-called partition walls that are adjacent to load bearing walls actually become bearing walls over time as the house settles and shifts. Then again, if there is a heavy AC unit above or if you are on the ground floor with lots of weight above, the issue becomes even more complicated.
There are also some great construction books that deal with this issue and contain charts of acceptable loads and beam types. One that has a good description of shoring and also beam/span information is "Renovation, A Complete Guide" by Michael W. Litchfield.