Yes. the Wayfaring Temple would die.
What happens is this, their temple is a 4/4 with no damage when the spell is cast because your opponent had 3 other creatures in play at the time. Since the temple is not a pirate, it takes two damage like everything else. Creatures with more damage on them than their toughness are sent to the graveyard as a state based action(SBA). Here's the relevant rule:
704.5g If a creature has toughness greater than 0, and the total damage marked on it is greater than or equal to its toughness, that creature has been dealt lethal damage and is destroyed. Regeneration can replace this event.
When SBAs are checked after Cannonade resolves, the two creatures with 2 or less toughness die due to this rule, but Wayfaring Temple does not. This is because at that point he is still a 4/4, since the other two are still alive. Because something happened as a result of SBAs, the SBA check is done again:
704.3. Whenever a player would get priority (see rule 116, "Timing and Priority"), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event. If any state-based actions are performed as a result of a check, the check is repeated
During this second round of SBA checks, Wayfairing temple is now a 2/2 due to the deaths of the other creatures with 2 damage on it, following 704.5g it dies during this round of checks. The fact that they die in different SBA rounds may matter, if one of the creatures that died in the first round of checks was something like Deathgreeter, it would not see the temple die. There would be a third round of SBA checks which, based on the information given, would do nothing and priority would pass back to the active player.
Note there are no "counters" involved in wayfaring temple, it's power is set by a characteristic defining ability.