Coronal active regions are observed to get increasingly fuzzy (i.e., increasingly confused and uniform) in increasingly hard energy bands or lines. We explain this as evidence of fine multi-temperature structure of coronal loops. To this end, we model bundles of loops made of thin strands, each heated by short and intense heat pulses. For simplicity, we assume that the heat pulses are all equal and triggered only once in each strand at a random time. The pulse intensity and cadence are selected so as to have steady active region loops (~3 MK) on average. We compute the evolution of the confined heated plasma with a hydrodynamic loop model. We then compute the emission along each strand in several spectral lines, from cool (<=1 MK), to warm (2-3 MK) lines, detectable with Hinode/Extreme-ultraviolet Imaging Spectrometer, to hot X-ray lines. The strands are then put side by side to construct an active region loop bundle. We find that in the warm lines (2-3 MK) the loop emission fills all the available image surface. Therefore, the emission appears quite uniform and it is difficult to resolve the single loops, while in the cool lines the loops are considerably more contrasted and the region is less fuzzy. The main reasons for this effect are that, during their evolution, i.e., pulse heating and slow cooling, each strand spends a relatively long time at temperatures around 2-3 MK and it has a high emission measure during that phase, so the whole region appears more uniform or smudged. We predict that fuzziness should be reduced in the hot UV and X-ray lines.