During the summer, my room can get hot. I think the max is 90s F, but lets set the limit to 100.

Do you think it is ok to have a machine running with 1 case fan and a fanless PSU reasonable?

I see the reviews are "tested in ambient room temperature, typically 20~24°C" from http://www.silentpcreview.com/article1220-page6.html

Sure, but as with fanless PSU's in general it depends even more on the makeup of the system. A bottom mounted PSU in a case with an exhaust in the upper part of the system should be fine in almost any humanly bearable situation. Keep it in the shade.

Hm, that is true. I was planning on getting the Solo II, but still researching on the options out there.

As mkk noted, it depends on the components you use. If your system components are similar to the Solo II reviewed here, just add 15C to those results and you'll be in the ballpark for your system. Probably fine for an IGP system, probably dodgy for a system with a gaming GPU (without additional airflow).

From a little research it will probably be:

CPU Intel Core i5-3550 @ 3.30GHz $209.99
Motherboard GIGABYTE GA-Z77MX-D3H LGA 1155 Intel Z77 HDMI SATA 6Gb/s USB 3.0 Micro ATX Intel Motherboard $129.99
RAM (16GB) $90
Case Antec Solo II $99.99
Video Card Radeon HD 7750 150


Currently my first near silent machine:

Operating System
MS Windows 7 Ultimate 64-bit SP1
CPU
Intel Core 2 Duo E8400 @ 3.00GHz 63 °C
Wolfdale 45nm Technology
RAM
8.00 GB Dual-Channel DDR2 @ 399MHz (5-5-5-18)
Motherboard
Gigabyte Technology Co., Ltd. P35-DS3L (Socket 775) 41 °C
Graphics
DELL E228WFP (1680x1050@60Hz)
VE247 (1920x1080@60Hz)
512MB GeForce 9600 GT (Elitegroup) 60 °C
Hard Drives
488GB Western Digital WDC WD5000AACS-00ZUB0 ATA Device (SATA) 37 °C
313GB Western Digital WDC WD3200BEKT-00KA9T0 ATA Device (SATA) 35 °C
1954GB SAMSUNG SAMSUNG HD204UI ATA Device (SATA) 35 °C
Optical Drives
PIONEER DVD-RW DVR-219L ATA Device
Audio
Realtek High Definition Audio

That's a low power GPU, only 55W TDP. You should be ok.. If you go with a passive version, you might need to strap a low rpm fan onto it for better airflow/cooling. Easy enough to test first and then tweak.

Also, you could consider getting a semi-passive PSU, where the fan only spins when temps get high/high load. Seasonic x 560, Kingwin LZP-550, etc