We present a new Spitzer transit observation of K2 - 28b , a sub-Neptune ( R _ { p } = 2.45 \pm 0.28 R _ { \earth } ) orbiting a relatively bright ( V _ { mag } = 16.06 , K _ { 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 \pm 0.20 R _ { \earth } ; ) . Our new 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 James Webb Space Telescope ( JWST ) observations . We also evaluate the system ’ s suitability for atmospheric characterization with 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 ( TESS ) and find K2 - 28b to be representative of the kind of mid-M systems that should be detectible in the TESS sample .