Electrical – mosfet driver uln2003

Well, ~1.6 Watts with a thermal resistance (junction to ambient) of say 40 Degrees Celsius per Watt makes it go from 25 degrees ambient to ~90 degrees which won't really kill it, but that assumes your calculations are perfect. The heat you see here is actually ALWAYS being dissipated while operating in your 4A load condition.

The absolute max ratings is 150 degrees, so during the 4 microsecond switching period, if it manages to generate a lot of heat, enough to bring the junction up to 150+, then it may begin to fail. Seems a bit of a fair stretch, especially if you only switch it a few times. If you are switching many times a second, this may build up average heat enough for it to fail fairly quickly.

Is very common to see two capacitors in parallel in regulators inputs and outputs. Large capacitors are usually electrolytic and they are used to filter out low frequency ripple and respond to reasonably fast load changes, however they are not good at filtering higher frequency noise, that is why the small capacitors (usuarlly ceramic and non-polarized) are used. These have an excellent high frequency response and noise filtering capabilities