  We present a thermodynamic study of the phase diagram of single-crystal
Ba1-xKxFe2As2 using specific heat measurements. In zero-magnetic field a clear
step in the heat capacity of deltaC/Tc = 0.1 J/f.u.K2 is observed at Tc = 34.6K
for a sample with x = 0.4. This material is characterized by extraordinarily
high slopes of the upper critical field of dHc2,c/dT= -6.5 T/K and dHc2,ab/dT=
-17.4 T/K and a surprisingly low anisotropy of gamma ~ 2.6 near Tc. A
consequence of the large field scale is the effective suppression of
superconducting fluctuations. Using thermodynamic relations we determine
Ginzburg-Landau parameters of kappac ~ 100 and kappaab ~ 260 identifying
Ba1-xKxFe2As2 as extreme type-II. The large value of the normalized
discontinuity of the slopes of the specific heat at Tc, (Tc/deltaC)times
delta(dC/dT)~ 6 indicates strong coupling effects in Ba1-xKxFe2As2.
