You may not need to worry about heat in this particular instance. The small board draw is roughly 0.5Watts which is pretty low. It might get warm, but I highly doubt it will get hot. This is more of a concern the the cheaper linear regulators mentioned above.
As far as over rating components go. Yeah, it's better to over-rate the supply, but providing 20A to a board that is rated to pull 0.035A is grossly overkill. You would be more than generous with anything that provides more than 1/8th of an Amp.
In any case, it may be worth looking at the board a little closer, if there are any components that may suddenly draw more power, you should over-compensate a little more.
As far as your gate setup is concerned, I'm a little curious why the board responsible for control during a power outage runs off a plug-in transformer...