brent,
Perry's used to have a good process control chapter in the 5th and 6th edition, which was changed for the worse (in my opinion) starting in the 7th edition. The old chapter rightly defined a control design procedure which concentrated on defining the nature and magnitude of disturbances (and deadtime) expected. It will be very possible to control to +/-0.5F with the right instrumentation and design if the process is not subject to excessive disturbances- I think this is along the lines of ash's comment. For example, if you are trying to control temp using steam that varies unpredictably in pressure or quality then you are unlikely to be successful regardless of how much cost and effort is spent on design and instrumentation.
Once the disturbances are quantified, you will be in a better position to assess ability to meet your objective. You can also gain significant advantages using calculated variables (like duty control) and feed forward action in addition to conventional PID cascades.
More detail of your process and design proposal could help in getting an opinion from the forum.
best wishes,
sshep