Hyper Threading does not effect whether you can or can't install Win8 because there are even versions of the newest Intel processors that doesn't include HT. It would all depend on which P4 you had. You can search for CPU-Z on google and download/install and it will it will tell you the exact P4 and chipset you have and then you can type that processor into the search box on ark.intel.com and it will list what features that particular processor has. It will support Win8 if at the bottom it has "Yes" beside the Execute Disable bit. But, you will have to make sure that the chipset and BIOS on your P4 machine will support a newer P4. The date of your BIOS version should be in CPU-z and the intel site will be able to tell you which processors your chipset supports. It will also need to support PAE which the intel site does not tell you. cpu-world.com will show you whether your particular processor supports PAE(physical address extensions) or not (if not on the spec tab then on the CPU id tab).
I've installed Win 7 Ultimate 32-bit on my old Dell Dim 8400 computer released in 2004. That Dell has P4 with HT. Win 7 worked fine with it.
What about the HT part? Would Win 8 even install? That Dell Dim 8400 already had many parts upgraded - vid card, RAM, DVD burner, and SATA HDD.
I think I said this is an earlier post, but I had the P4 540 and that does not have the bit that is required and so in order to beable to use Win8. I updated my BIOS and upgraded to a P4 650 refurbished and now Win8 runs just fine. It is even faster than Win7 and as icing on the cake, the processor I upgraded to was 64bit capable. So the $9 I spent on the new processor was well worth the effort to beable to upgrade to Win8. I was a little worried about it being refurbished but having ran it non-stop since January I haven't had a problem with it.