Is there anyway to set the keypad to automatically lock after a short time?

Set a password in security options and set the time out to a suitable value for you.

(The screen will still turn on if a key is pressed to request the password, but it won't stay on.)

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I want to be able to automatically lock and then easily unlock the keypad (without a password), just so that it doesn't accidentally dial in my pocket.

Short of an after-market app, the only way I know to do what you want with the stock OS is with a password. Don't know about any third-party apps. Have you browsed app world, maybe starting in the utilities section?
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You can simply lock the keypad by holding the 'a' key when you finish with the device. It is then unlocked with the lock button on the top. I have found this works very well once you become used to it. A password is not required for this functionality.

OP understands that...the question is how to automate it on a time out
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Those are the two choices... only two choices to achieve a locked keyboard.

My bad. You could try this I imagine, although it says it is for the pearl there have been other members using it on devices other than the pearl.

AutoLock for BlackBerry