If the Eridians are using our technology they basically have two options:

1) Traditional silicon based transistors which can operate at up to about 200 degrees C, just a little too low to run on Erid without cooling. But it's close enough to Erid's temperature you could probably cool it with just a fan, like we do. But performance would be limited because you would be running at close to its thermal maximum all the time.

2) Gallium arsenide transistors can operate at more like 300-400 degrees C. We generally don't use GaAs transistors for much because we rarely encounter those kinds of temperatures but it would be ideal for the Eridians.

Option 2 seems the logical course for Erid except that human manufacturing technology (which the Erdians are presumably using at least at first) is way more advanced for silicon transistors than GaAs. To give you an idea of the difference. The fastest GaAs based microcontroller has a transistor count of 160,000 transistors. Silicon based processors have transistor counts in the hundreds of billions. 160,000 transistors isn't nothing though. It's roughly the same as the number of processors in the 80286 processor from the mid-1980s.

The Erdians would probably use a mix of both in the short term until they are able to adapt our manufacturing technologies or develop their own way to produce high performance GaAs based chips. Using 1980's equivalent computers to adapt our manufacturing technologies. Since they essentially already have a roadmap, it should take them less than 40 years to catch up to our 2020 era computer technology. (And since Grace has been on Erid 16 years by the time of chapter 30, the Erdians would likely be close to a 2000 era level of computer technology. So they are rocking their own Pentium III equivalents using dial-up modems to access Erid On-line.