I don't see the need for unique_ptr for the root node.

spNode root;

I would just make this a node.

Node root;

The use of std::map is fine. But it does have O(log(n)) lookup. If you switch back to an array its O(1). Its a time for space thing. Pick the one you want.

I don't like the two line creation of nodes.

        std::unique_ptr<Node> node(new Node());
        temp->children[c] = std::move(node);

Just use reset:

        temp->children[c].reset(new Node());

Or if you have C++17 use std::make_unique()

        temp->children[c] = std::make_unique<Node>();

Personally search() does not seem quite the correct verb.

bool search(const std::string& str);

What is wrong with find()?

I don't see the need for unique_ptr for the root node.

spNode root;

I would just make this a node.

Node root;

The use of std::map is fine. But it does have O(log(n)) lookup. If you switch back to an array its O(1). Its a time for space thing. Pick the one you want.

I don't like the two line creation of nodes.

        std::unique_ptr<Node> node(new Node());
        temp->children[c] = std::move(node);

Just use reset:

        temp->children[c].reset(new Node());

Or if you have C++14 use std::make_unique()

        temp->children[c] = std::make_unique<Node>();

Personally search() does not seem quite the correct verb.

bool search(const std::string& str);

What is wrong with find()?