apple tv that I got a couple of months ago
What is the model Apple TV box?
Identify your Apple TV model - Apple Support
Find your Apple TV model number - Apple Support
For newly bought devices from Apple or Apple Authorized Resellers, you would get priority Support for the first 90 days, to help you get going with it (wider support than just hardware malfunctions). Apple Complimentary Support - Official Apple Support
For newly bought devices from Apple or Apple Authorized Resellers, you would get 1 year limited warranty for manufacturing issues.
If you purchased AppleCare+ with your device, you would get additional hardware support and perks, and for a longer time.
Apple TV repair & service - Apple Support
restarting randomly
When this happens, does the status light go out, then start blinking for ~15 sec or so, before glowing continuously again? If not, then it wouldn’t have been an actual device restart, but something else that possibly gets it to show a black screen.
Please review: If your Apple TV isn't working, won't turn on, or shows a black screen - Apple Support
Is this something I should take to Apple …
From your description, yes, you should talk to Apple about it.
Contact Apple for support and service - Apple Support (phone numbers)
Get support - Apple Support (start your [software] support request online)
If the Support staff asserts that it probably is a software issue, then consider a ‘factory reset’ for the device. Reset or restore your Apple TV to its factory settings - Apple Support
Get support - Apple Support (start your [hardware] support request online)
If the Support staff asserts that it probably is a hardware issue, then take the device in to Apple (or mail it in, if they offer that). For going to a retail store, it is best to make a reservation then. Genius Bar reservation and Apple Support options - Apple