Something like this should do:
$tempdir = "temp#" + ("{0:d5}" -f (Get-Random)).Substring(0,5)
New-Item -ItemType Directory -Path "$env:USERPROFILE\Desktop\$tempdir"
If you want to be able to create such a directory in any folder, you could add a Create Temp Directory entry to the folder context menu:
Windows Registry Editor Version 5.00
[HKEY_CLASSES_ROOT\Directory\shell\mktemp]
@="Create Temp Directory"
[HKEY_CLASSES_ROOT\Directory\shell\mktemp\command]
@="\"C:\\windows\\system32\\WindowsPowerShell\\v1.0\\powershell.exe\" -Command \"& {New-Item -ItemType Directory -Path ($args[0] + '\\temp#' + (\\\"{0:d5}\\\" -f (Get-Random)).Substring(0,5))}\" %1"
Replace HKEY_CLASSES_ROOT
with HKEY_CURRENT_USER\Software\Classes
if you want to apply the modification to your user only.