Sometimes when I access my windows azure website, the initial response time is very slow. After the first page load the website is fast. Some background: The website is not
If you only need to warm it up once (vs keeping it warm) and are mostly trying to prevent your customers experience page cold starts, I believe the correct tool is IIS Application Initialization. You can configure it with a list of urls to hit before it deems the app ready for action.
My site is suffering from page cold starts and that is severely magnified in Azure Websites (even on an S3), but it is absolutely speedy after its served that first time thanks to several layers of caching (our inefficient use of Umbraco's dynamic nodes query language creates a lot of database churn--which we're cleaning up opportunistically).
From what I've read and my own web.config attempts this is still not available in Azure Websites. I've asked Microsoft for it here: MS IDEA: Application Initialization to warm up specific pages when app pool starts. Please consider voting for it.