Can rate constant for forward reaction be equal to rate constant for backward reaction? For a particular reaction, can we have
$K_c = 1$?

My confusion arised when I was studying the effect of temperature on $K_c$ . I see that the temperature must affect forward and backward rate constants, differently for a reaction so that it changes $K_c$ (which is ratio of the two rate constants). So I thought for a reaction with $K_c$ equal to one, both the rates must be equal, so both will get equally affected by temperature, and thus no change in $K_c$ , or does it have something to do with the Arrhenius equation?

I know that there is a lot of lacking in my intuition as I have just began studying Le Chatelier's principle and all the stuff. So a detailed explanation would be much welcome.
When forward and backward reaction have the same rate, $K_c$ is equal to $1$ in the case of a reaction where the total number of reactants is equal to the total number of products in the chemical equation describing the change. If the total of these stoichiometric coefficients is not the same before and after the horizontal arrow, $K_c$ may be equal to $1$, but must have a dimension, like mol/L or L/mol, or any combination of these units. 

As the forward and backward rections have different activation energies, their rates change differently with increasing the temperature. So the equilibrium constant $K_c$ can be equal $1$ at only one temperature.