This worked for me...

RestTemplate restTemplate = new RestTemplate(getClientHttpRequestFactory());

private ClientHttpRequestFactory getClientHttpRequestFactory() {
    int timeout = 5000;
    HttpComponentsClientHttpRequestFactory clientHttpRequestFactory
      = new HttpComponentsClientHttpRequestFactory();
    clientHttpRequestFactory.setConnectTimeout(timeout);
    return clientHttpRequestFactory;
}

To achieve calling rest template with timeout, first you should create config class also use with @Bean annotation, then implement in class and call with RestTemplateConfig.

@Configuration
public class RestTemplateConfig {

    @Bean
    public RestTemplate restTemplate() {
        return new RestTemplate(clientHttpRequestFactory());
    }

    private ClientHttpRequestFactory clientHttpRequestFactory() {
        HttpComponentsClientHttpRequestFactory clientHttpRequestFactory = new HttpComponentsClientHttpRequestFactory();
        clientHttpRequestFactory.setConnectionRequestTimeout(4000);
        clientHttpRequestFactory.setReadTimeout(4000);
        clientHttpRequestFactory.setConnectTimeout(4000);
        return clientHttpRequestFactory;
    }
}

But I suggest you use Apache HttpClient, you can manage the connection pool, keep-alive, idle monitor and also create custom error handler. You can check the link: https://springframework.guru/using-resttemplate-with-apaches-httpclient/

You can also modify the SimpleClientHttpRequestFactory.

RestTemplate restTemplate = new RestTemplate();
restTemplate.setRequestFactory(customHttpRequestFactory());

private SimpleClientHttpRequestFactory customHttpRequestFactory() {
    SimpleClientHttpRequestFactory simpleClientHttpRequestFactory = new SimpleClientHttpRequestFactory();
    simpleClientHttpRequestFactory.setReadTimeout(2000);
    simpleClientHttpRequestFactory.setConnectTimeout(2000);
    return simpleClientHttpRequestFactory;
}