I was attempting something similar, and the RoboSpice example helped me work it out:
HttpHeaders headers = new HttpHeaders();
headers.set("Accept", "application/json");
HttpEntity<String> request = new HttpEntity<>(input, createHeader());
String url = "http://awesomesite.org";
Uri.Builder uriBuilder = Uri.parse(url).buildUpon();
uriBuilder.appendQueryParameter(key, value);
uriBuilder.appendQueryParameter(key, value);
...
String url = uriBuilder.build().toString();
HttpEntity<String> response = restTemplate.exchange(url, HttpMethod.GET, request , String.class);