A column of a datagrid can handle all attribute types. While a Template grid uses the input widgets to display the attribute value. Since each input widget can handle a specific (set) of attribute types the attributes you can connect is limited to those. I guess that is limiting your options.
Instead of adding an input widget and then connecting it to an attribute, select the area (not a widget) where you want to display the attribute and just drag and drop an attribute from the connector into that area. The modeler will automatically pick the right widget.
You should be able to get all of the attributes from the temp entity in either the template grid or the data grid. Can you share some screen shots of the domain model (with the temp entity) and the page(s) with the template grid and data grid? This will help in troubleshooting.
Can't reproduce it. By temp entity you mean a non-persistent entity.