Both reactions occur via preliminary formation of the indanone-enol salt, which reacts with diethyl carbonate, through conjugation and leads to C-substitution. But both reactions are highly exothermic and therefore, reactants are slowly added, in order to prevent any uncontrolled, exothermic heat. After the end of the reactants addition, the reaction mixture is gradually heated, in order to offer an amount of heat that is equal to the activation energy (minus the exothermic heat) and thus, the reaction is completed.
Theoretically, both reactions can effectively occur at room temperatures in high dilution but NaH is not compatible with diethyl carbonate; in contrast to t-BuOK, which is.