Greetings!
We appreciate your question about the wireless capabilities of this Samsung range model.
Yes, your phone through the SmartThings app will receive a notification when the oven has reached the desired temperature that was set. Notifications have to be enabled for the SmartThings app on your phone for push notifications to work.
I have shared a Samsung link below that will give more information about notifications via the SmartThings app.
Manage SmartThings notifications, messages, and activities:
https://www.samsung.com/us/support/troubleshooting/TSG01110148
Should you need more assistance, please feel free to get back to us via the following options:
1. Facebook Messenger: http://m.me/samsungsupport
2. Twitter: https://twitter.com/messages/compose?recipient_id=18768513
3. Samsung Community: https://us.community.samsung.com/t5/Samsung-Community/ct-p/us
When you message us, provide us with this reference number 1145068700, it will help our team pull up your information.
Leo