Is the deprotonation of phenol exothermic?
Any bond dissociation reaction is endothermic, hence the termin 'bond'. Heterolytic dissociation (into ions) is more endothermic than homolytic. Strong acids are not exception.

However, the words above are about molecules in vacuum. When the molecules are in a media, interaction with media may stabilize ions strongly. This is why salts dissolve and acids/bases dissociate.

In case of phenol, dissociation in vacuum is definitely endothermic. Dissociation in water is also endothermic, since the dissociation constant is small. (1) However, deprotonation implies that protons moves to another acceptor, and in this case it depends entirely on the acceptor. Similarly, in nonwater media dissociation of phenol also may be exothermic. 

(1) Dissociation constant is tied to dissociation free energy with law 
$\ln K_e = - \Delta G / RT$ . Since entropy in reaction dissociation reactions is definitely increasing, the only reason for $\Delta G$ to be unfavorable is enthalpy.