Or talk to your DM about finding/creating a suit of full plate that you can summon onto yourself as a bonus action.
I am the DM.

In 4e there actually was armor you could don and doff as an action.
Yeah. Some nice solutions. And still no one found a way to make that feature useful.
Just for others to make my intentions clear:
I have no problems finding a houserule solution. It is very easy to find one.
I also don't want to talk about balance concerns or how the wizard survived until then.
I also believe donning heavy armor is risky, because you need to maintain concentration.
Fact is however: RAW there is an explicitely stated feature which is useless for now without house ruling or very lenient interpretation of rules. (At what point in those 10 minutes needed to don armor you are actually wearing too much armor to cast spells.)
Mage armor and decent dexterity will be enough for the wizard usually. You can also wield a shield with your rapier.
You can't use your shield spell anymore but 50 temp hp might take care of that. A war mage has other means of using its reaction.
And still that heavy armor feature needs some love.
My personal favourite:
When you cast that spell, (pieces of) a suit of armor you have nearby wraps around you and is held in place by magical force. If the spell ends, that armor falls off immediately.
Maybe a miniature suit of armor would be even better. Make it a costly optional spell focus.