How can I force a download of a pdf in a url?

I have a URL that goes to a pdf file. In my coldfusion page, I want to allow the user to download the file (using the open/save dialog or however that particular browser handles it).

This is the code I have so far:

<cfset tempFile = getTempFile(getTempDirectory(), 'testfile') />
<cfhttp url="myUrl/myFile.pdf" method="get" file="#tempFile#"/>

<cfheader name="Content-Disposition" value="attachment; filename=myFile.pdf">
<cfcontent type="application/pdf" file="#tempFile#">

This seems to work... but when I try to open the file it tells me something's wrong with the file. What am I doing wrong?