Sed replace entire line after match in XML

I want to replace a line in an XML once I identify the correct tag.

Take

<root>
    <My_Name>Andrew</My_Name>
    <My_Age>94</My_Age>
</root>

I would like to replace Andrew with Bob

where Bob is stored in $nameVariable

Using sed,

sed -i 's/<My_Name>.*</My_Name>/<My_Name>$nameVariable</My_Name>/g'

This is probably failing due to the lack of escape characters, which I've tried putting in different places, but don't seem to get them right. Help would be much appreciated.