We have applied the principles of indirect stellar surface imaging (Do
ppler imaging) for simulated mapping of active regions in the upper at
mosphere of cool active stars. Our tests illustrate how synthetic dist
ributions at the chromosphere or transition region level can be recove
red from time series of high resolution profiles of UV lines, as satel
lites like IUE, HST or PRISMA could collect them. Due to the large wid
th of intrinsic profiles in such regions of the atmosphere, we find th
at only stars with a projected equatorial velocity v sin i larger than
about 20 km s-1 can be mapped with this method. For all other stars,
only large scale equatorial features can be recovered. Increasing spec
trum quality improves the reconstruction significantly, especially in
the case of high latitude features. We also find that data should span
several successive rotational cycles in order to minimise the impact
at the reconstruction of all intrinsic random variations of UV lines f
ormed in the chromosphere or transition region. Finally, we show how m
apping can be affected by the existence of flows in the upper atmosphe
re.