  This paper presents late-time near-infrared and {\it Spitzer} mid-infrared
photometric and spectroscopic observations of warm dust in the Type IIn SN
2005ip in NGC 2906. The spectra show evidence for two dust components with
different temperatures. Spanning the peak of the thermal emission, these
observations provide strong constraints on the dust mass, temperature, and
luminosity, which serve as critical diagnostics for disentangling the origin
and heating mechanism of each component. The results suggest the warmer dust
has a mass of $\sim 5 \times 10^{-4}~$\msolar, originates from newly formed
dust in the ejecta, or possibly the cool, dense shell, and is continuously
heated by the circumstellar interaction. By contrast, the cooler component
likely originates from a circumstellar shock echo that forms from the heating
of a large, pre-existing dust shell $\sim 0.01 - 0.05$~\msolar~by the late-time
circumstellar interaction. The progenitor wind velocity derived from the blue
edge of the He 1 1.083 \micron~P Cygni profile indicates a progenitor eruption
likely formed this dust shell $\sim$100 years prior to the supernova explosion,
which is consistent with a Luminous Blue Variable (LBV) progenitor star.
