I had the same issue with iOS 10.0.2 on an iPhone 6s. It began with the latest 10.0.2 update, not with the initial upgrade from iOS 9 to iOS 10 (either that or I simply didn't notice it until 10.0.2).
Symptoms:
After the Phone App is inactive for more than 1 hour, launching the Phone App will cause it to hang and eventually crash (just closes) after a varying amount of time in "hung" state. During the time the Phone App is hung, no touches register within the App. The home button still functions and app switching works as expected, but until the Phone App is terminated or times out, it remains unresponsive.
Research:
I've spend some time researching this issue and after reading a bunch of comments on this thread even considered a full factory reset. Instead, however, I decided to do the work of an iterative approach of testing to see if the issue is actually related to the Contacts App than the Phone App itself. To do this, I went into Settings->Mail, Settings->Facebook, Settings-iCloud and for each Synced account turned off Contacts Sync and then opted to delete the contacts form the phone. I then open the Contacts App and ensure there are no contacts shown. Essentially now the iPhone's Phone App history just showed numbers without any names. Same goes for the iMessage App. I then re-tested to see if the issue with the Phone App freezing would recur and it did not.
I waited 3 days and rebooted my phone several times to ensure that the Phone App freezing issue would not return and with all contact sync accounts removed and the Contacts App completely empty, the Phone App did not exhibit freezing a single time over the 3 day period.
I then slowly re-enabled each synced contacts account one account at a time.
Resolution:
After re-enabling contact sync for each account one at a time, I found that after re-adding contact sync on an outlook.com mail account, the issue with my Phone App freezing returned. Therefore I am tentatively concluding that either the issue is related to Outlook.com account Contacts syncing or more specifically a perhaps malformed contact part of my Outlook.com account. I am currently testing my iPhone with contact Sync for the outlook.com account disabled and have not seen the Phone App freezing issue.
Hope it helps,
David V.
TLDR: Try disabling just contact sync on each of your synced accounts one at a time and re-enable one at a time slowly to find the account that may be causing the issue.
