You could wrap the not-bold text into a span and give the span the following properties:
.notbold{
font-weight:normal
}
and
<h1>**This text should be bold**, <span class="notbold">but this text should not</span></h1>
See: http://jsfiddle.net/MRcpa/1/
Use <span> when you want to change the style of elements without placing them in a new block-level element in the document.