Three-dimensional direct numerical simulations of fuel-lean (equivalence ratio φ = 0.24) hydrogen/air turbulent catalytic combustion were carried out in a platinum-coated planar channel with isothermal walls and an incoming fully-developed turbulent flow, at two inlet bulk Reynolds numbers (Re_H = 5700 and 12,360 based on the channel height H) and four global catalytic reaction rates. The turbulent flow laminarization due to heat transfer from the hot catalytic walls was appreciable, with turbulent intensities dropping by 37% and 25% at the channel outlet for the low and high Re_H, respectively. The ratio of the local average turbulent hydrogen conversion rate to the corresponding local laminar conversion rate (〈ṡ̇_T〉/ṡ_L) was found to be a monotonically increasing function of streamwise distance, Reynolds number ReH, and catalytic reactivity. Despite the turbulent flow laminarization, 〈ṡ_T〉/ṡ_L ratios at the channel outlet reached values up to 170% for the highest Re_H = 12,360 and for infinitely-fast catalytic chemistry. A correlation was further established for the ratio of the turbulent hydrogen conversion rate at finite-rate chemistry to the corresponding turbulent conversion rate at infinitely-fast chemistry. The instantaneous local catalytic reaction rates exhibited large fluctuations, which were up to 300% and 500% for the low and high Re_H, respectively. Fourier analysis indicated that a diminishing catalytic reactivity acted as a low-pass frequency filter for the overlying fluctuations of the turbulent flow.