There is no obvious direct connection between catalytic properties and stability of an enzyme.
You are trying to make a connection, but let's consider your statement:
Then the Arrhenius equation can be used to describe how the rate constant of an enzymatic reaction changes with temperature.
According to the Arrhenius equation, all reactions (catalyzed by an enzyme or not) become faster as temperature increases. The higher the activation energy, the more pronounced the increase. However, if the enzyme unfolds, it will no longer catalyze the reaction.
But how can I use this information to decide whether the more catalytic enzyme is more or less temperature dependent?
The biggest temperature dependence occurs at the temperature where the enzyme unfolds. There is the idea that enzymes have to be flexible to be effective catalysts, so there might be a correlation between optimal temperature for the activity and the unfolding temperature. The best way to figure this out would be to compare enzymes from mesophiles and thermophiles in terms of optimal temperature for catalysis vs melting temperature.