If I use this construction:
<xsl:apply-templates select="$var">
<xsl:with-param name="title" select="'new-value'"/>
</xsl:apply-templates>
Templates are applied Ok, but parametes are not passed.
If select-expression doesn't use variables (select some nodeset inside 
this document), parameters works Ok too.

Here is three files to reproduce bug:
======================= test.xsl ==
<?xml version="1.0"?>
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" 
version="1.0">
<xsl:variable name="var" select="document('a.xml')"/>
<xsl:template match="root">
	<out>
		Here is output with default title:
		<xsl:apply-templates select="$var"/>
		Here is output with 'new-value' title:
		<xsl:apply-templates select="$var">
			<xsl:with-param name="title" select="'new-value'"/>
		</xsl:apply-templates>
	</out>
</xsl:template>
<xsl:template match="a">
	<xsl:param name="title" select="'default'"/>
	<a-template>
	<title><xsl:value-of select="$title"/></title>
	<was-a><xsl:value-of select="."/></was-a>
	</a-template>
</xsl:template>
</xsl:stylesheet>
===================================
======================= test.xml ==
<?xml version="1.0"?>
<root/>
===================================
========================== a.xml ==
<?xml version="1.0"?>
<a>some text in a-tag</a>
===================================