  We present a new {\em Spitzer} transit observation of K2$-$28b, a sub-Neptune
($R_{\rm p} = 2.45\pm0.28 R_{Earth}$) orbiting a relatively bright ($V_{\rm
mag} = 16.06$, $K_{\rm mag} = 10.75$) metal-rich M4 dwarf (EPIC 206318379).
This star is one of only seven with masses less than 0.2 M_{Sun} known to host
transiting planets, and the planet appears to be a slightly smaller analogue of
GJ 1214b ($2.85\pm0.20 R_{Earth}$; \citealt{2013A&A...549A..10H}). Our new {\em
Spitzer} observations were taken two years after the original K2 discovery data
and have a significantly higher cadence, allowing us to derive improved
estimates for this planet's radius, semi-major axis, and orbital period, which
greatly reduce the uncertainty in the prediction of near future transit times
for the {\em James Webb Space Telescope} ({\em JWST}) observations. We also
evaluate the system's suitability for atmospheric characterization with {\em
JWST} and find that it is currently the only small (< 3 R_{Earth}) and cool ($<
600$ K) planet aside from GJ 1214b with a potentially detectable secondary
eclipse. We also note that this system is a favorable target for near-infrared
radial velocity instruments on larger telescopes (e.g., the Habitable Planet
Finder on the Hobby-Eberly Telescope), making it one of only a handful of
small, cool planets accessible with this technique. Finally, we compare our
results with the simulated catalog of the Transiting Exoplanet Survey Satellite
({\em TESS}) and find K2$-$28b to be representative of the kind of mid-M
systems that should be detectible in the {\em TESS} sample.
