I just had fans blowing out a window
At the end of the day, I suspect that's what this is about to look like.
Personally I'd just grab the tube from a portable AC unit (think flexible dryer vent pipe) since it usually comes with a window block (you'll know what I mean when you see it). If you want to go really slick drop a 120mm (or whatever fits) PC fan at either end to help with the out air pressure / backpressure / draft ... whatever it's called.
And definitely look into a heat pump and/or A/C unit. The world is just going to get hotter and having one really helps with the resale value of the property. FYI the portables aren't as good, but they are useful and fairly cheap since you don't need to install anything. Just watch your BTUs vs your breaker box. 14k+ can cause issues with older (read 1970s and before) boxes since they have a decent draw spike when they 1st come on.
A central AC unit is in the plans. It's just not this year, or maybe next. Unless things get really bad. We bought this house in November and the furnace went out within the first weekend. So we had to replace that. And had them do the work at the time to make room for an AC later. But between the furnace, replacing ALL the windows, and maybe painting the exterior this year. There's just not enough free cash flow for an AC unit. Hence the "How can I get the heat out of the room quickly and easily?"
I would just do a window fan unless it gets super hot then window AC. More often enough this just running all the time will keep the room cool enough especially if its cool outside already but just hot in the room due to the PC.
I have a portable AC unit with a vent hose that can be put out the window, which I guess will work for now. I just have to rearrange things in the room next weekend to make that work. Which is fine, I was going to swap out this desktop anyways. Might as well get a window seal with 2 fan hose ports and do it that way all at the same time.
I had the same problem for years in my previous office space in this house. The previous office was in a finished attic room, and the central A/C just doesn't have the guts to push the air that high, very efficiently. It would easily exceed 80F in that room when gaming on the PC.
I thought of all the options you did as well, but in the end I just installed a window AC. The one I used was a cheaper unit and was loud as hell, but it cooled the room VERY fast and easily got the job done. I often had the room at 68F.
Since covid, I've been working from home and often on the phone with customers. I took a spare room in the house and made a new office, but was so fed up with how hot and loud the PC had been, that I didn't even want it in the same room as me any more. I actually ran the cables through the wall to the guest bedroom and the PC sits in there, with USB and HDMI cables passing through the wall via modified outlet covers. It's whisper quiet in here and comfortable, always.
Long story...but I wasn't sure if that was an option for you too. I feel your pain. It was annoying dealing with that.
I don't know if putting the PC in another room is an option in my situation but it's an interesting thought. Later this year, I have a downstairs area I'm going to turn into a home theater where I might do something similar.
For everyone who did the window unit thing: Out of curiosity was it a window unit that sat in the window permanently? Or a hose venting out of a window seal kit?
If you did the window seal kit, any tips on how to make that stay put so that you can open the windows the rest of the way if it's nice outside?
The sit-stand desk in front of the window is about to move to the right, up against the wall. The printer stand there is going in the closet behind me. With the portable AC sitting somewhere on the right with a hose running under the desk against the wall out the window.