From your dashboard, go to design and into Edit Html. Make sure that you have ticked the Expand Widget Templates checkbox on the top right. Now you have to find the widget ID of the widget title you wish to edit. To find the ID of the gadget you wish to modify, please read this previous post here.
For example, the widget id for my widget is Label1, you will find something similar to this code below:
<b:widget id='Label1' locked='false' title='Topics' type='Label'>
<b:includable id='main'>
<b:if cond='data:title'>
<h2><data:title/></h2>
</b:if>
<--------------lots of data here that you don't need--------------------->
</b:if>
<b:include name='quickedit'/>
</div>
</b:includable>
</b:widget>
</b:if>
<b:include name='quickedit'/>
</div>
</b:includable>
</b:widget>
Replace the data:title tag ( <data:title/> ) with the code below:
<img src="YOUR_TITLE_IMAGE_URL" alt="YOUR_GADGET_TITLE"/>
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