Hi MattFranklin,
Please create a folder name "MyTemp" under your site root, and set it for the TempDirectory property like below. Then give the full permission to user "Everyone" of this folder and try again. It will fix this error.
<CuteWebUI:UploadAttachments ID="uploader1" runat="server" TempDirectory="~/MyTemp" >
</CuteWebUI:UploadAttachments>
Regards,
Ken