In principle, 4-strokes should all run at the same temperature, so the differences you might be observing come down to usage: one tends to rev the lower-capacity engine much more, hence the higher temperatures.
What kind of "bigger 4-stroke" are we talking about here?
2-stroke engines have lower compression ratios, so they generally run a little cooler, but during race conditions the temperature should be very close to that of a four-stroke.