Hi Ken,
Strictly speaking, according to the NatSemi datasheet, neither capacitor is required
for the regulator to operate. However, the datasheet recommends a 0.22uF on the
input "if the regulator is located far from the power supply filter", which in your case,
is unlikely and "although no output capacitor is needed for stability" one "does
help transient response" and they recommend a 0.1uF ceramic capacitor.
See
http://www.national.com/ds/LM/LM340.pdf
You will certainly have to be careful with any noise from the fan and in any case,
always using capacitors represents good practice. Use a 0.22uF tag tantalum of appropriate
voltage rating (e.g. 35V) and low ESR on the input. Use a ceramic 0.1uF bypass cap on the output.