We study the properties of charmonium states at finite temperature in quenched QCD on large and fine isotropic lattices. We perform a detailed analysis of charmonium correlation and spectral functions both below and above T-c. Our analysis suggests that both S wave states (J/psi and eta(c)) and P wave states (chi(c0) and chi(c1)) disappear already at about 1.5T(c). The charm diffusion coefficient is estimated through the Kubo formula and found to be compatible with zero below T-c and approximately 1/pi T at 1.5T(c) less than or similar to T less than or similar to 3T(c).
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