METHODS

1. Changing only the index.php
2. Changing the admin interface for the template protostar: module, language (labels, description, name) and the index.php

METHOD 1 - CHANGING ONLY THE INDEX.PHP

1. Locate the index.php under the "joomla root"/templates/protostar
   use an ftp program to browse the server folders of your site
2. Edit the index.php
   You can use a simple notepad or a better editor like notepad++
3. Search for "google" word
4. Now we have to duplicate the line with the link to the fonts.googleapis.com/css?family and insert the font for the body
5. See the following code and images. 

<?php
// Use of Google Font
if ($this->params->get('googleFont'))
{
?>
	<link href='//fonts.googleapis.com/css?family=<?php echo $this->params->get('googleFontName');?>' rel='stylesheet' type='text/css' />
	<link href='//fonts.googleapis.com/css?family=Mako' rel='stylesheet' type='text/css' />
	<style type="text/css">
		h1,h2,h3,h4,h5,h6,.site-title{
			font-family: '<?php echo str_replace('+', ' ', $this->params->get('googleFontName'));?>', sans-serif;
		}
		body {
			font-family: Mako, sans-serif;
		}
	</style>

 You have to enable the google font for heading, as you can see it is inside an if ...

Screenshots method 1

METHOD 2 - CHANGING THE ADMIN INTERFACE

This way is more elegant and flexible way.

Goal is add a field on template Manager for the protostar: Google Font for Body

New field in the module of the Template Manager

Edit the file templateDetails.xml located in the folder /templates/protostar.

The fierst field is the original field, I duplicated it and changed the name, label and description.

<field name="googleFontName" class="" type="text" default="Open+Sans"
label="TPL_PROTOSTAR_FONT_NAME_LABEL"
description="TPL_PROTOSTAR_FONT_NAME_DESC" />
					
<field name="googleFontNameBody" class="" type="text" default="Open+Sans"
label="TPL_PROTOSTAR_FONT_NAME_BODY_LABEL"
description="TPL_PROTOSTAR_FONT_NAME_BODY_DESC" />

Language Override

Create one or more file on /administrator/language/overrides

• en-GB.override.ini
• it-IT.override.ini
• and so on...

In alternative you can use the Joomla Language Override Interface under the menu Components. BTW after you created the file you fille find the entries in component->Language->Override.

TPL_PROTOSTAR_FONT_DESC="Load a Google font for the headings and body (H1, H2, H3, etc. and BODY)"
TPL_PROTOSTAR_FONT_LABEL="Google Font for Headings"
TPL_PROTOSTAR_FONT_NAME_BODY_DESC="Example: Open+Sans or Source+Sans+Pro"
TPL_PROTOSTAR_FONT_NAME_BODY_LABEL="Google Font Name Body"

index.php

Locate the index.php under the "joomla root"/templates/protostar 
use the ftp to browse the server folders of your site

<?php
	// Use of Google Font
	if ($this->params->get('googleFont'))
	{
	?>
		<link href='//fonts.googleapis.com/css?family=<?php echo $this->params->get('googleFontName');?>' rel='stylesheet' type='text/css' />
		<link href='//fonts.googleapis.com/css?family=<?php echo urlencode($this->params->get('googleFontNameBody'));?>' rel='stylesheet' type='text/css' />
		<style type="text/css">
			h1,h2,h3,h4,h5,h6,.site-title{
				font-family: '<?php echo str_replace('+', ' ', $this->params->get('googleFontName'));?>', sans-serif;
			}
			body {
				font-family: '<?php echo str_replace('+', ' ', $this->params->get('googleFontNameBody'));?>', sans-serif;
			}
		</style>

The php urlencode(...) is useful to prevent a blank space on font name. It will works but will generate an error on html5 validation.

Please add urlencode(...) also in the first link. 

Screenshots method 2

IMPORTANT NOTE

Since Joomla 3.4.3 my google body fonts does not work.

I had to create a new style /style just before the /head and I copied inside the body style. This is not so elegant but it's the last work around found  ;-)