  We look at observational constraints on the thawing class of scalar field
models proposed to explain the late time acceleration of the universe. Using
the recently introduced `Statefinder Hierarchy', we compare these thawing class
of models with other widely studied dark energy (and modified gravity) models
to check the underlying parameter degeneracies. We put constraints on the
deviations of these thawing models from the canonical \Lambda CDM model using a
large class of observational data, e.g, the Supernova Type Ia data, the BAO
data, the CMB data and data from the measurements of the Hubble parameter using
red-envelope galaxies. We also forecast constraints using a simulated dataset
for the future JDEM SNe survey. Our study shows that, although with current
data it is difficult to distinguish different thawing models from \Lambda CDM,
a future JDEM like mission would be able tell apart thawing models from \Lambda
CDM for currently acceptable values of \Omega_{m0}
