Fujitsu Siemens (and other computer manufacturers) usually only spec PSU’s sufficient to get the job done without any overhead for more powerful CPU’s etc. You will need a new PSU.
Some of the older Fujitsu Siemens desktops came with non standard power supplies. Non standard in that they were long & thin instead of the more ‘normal’ ATX standard shape (15cm wide x 8cm high x approx 14cm deep). If you have to replace the PSU then available replacements will normally only be ATX standard and may not fit in your case.
You’ll probably have to do an operating system re-install as well…
Having said that, the CPU in that package is massively more capable than any P4 chip and bundled with a decent amount of memory so the value is there, it’s just the practicalities of getting it done.