We built a transient absorption spectrophotometer that can determine transient absorption spectral changes that occur at times as fast as approximately 200 ns and as slow as a minute. The transient absorption can be induced by a temperature-jump (T-jump) or by optical pumping from the deep ultraviolet (UV) to the infrared (IR) by use of single ns Nd:YAG laser pulses. Our use of a fiber-optic spectrometer coupled to a XeF flashlamp makes the collection of transient spectra easy and convenient in the spectral range from the near IR (1700 nm) down to the deep UV (200 nm), with high signal-to-noise (S/N) ratios. The spectral resolution is determined by the specific configuration of the fiber-optic spectrometer (grating groove density, fiber diameter, slit width) and varies between 0.3 and 10 nm. The utility of this spectrometer was demonstrated by measuring the rate at which a polymerized crystalline colloidal array (PCCA) of poly(N-isopropylacrylamide) nanogel particles optically switch light due to a T-jump induced by nanosecond 1.9 microm laser pulses. In addition, we measured the rate of optical switching induced by a 3 ns 355 nm pump pulse in PCCA functionalized with azobenzene.