How to correctly specify a range of temperatures in both Fahrenheit and Celsius?

Current icky wording:

... they do best in temperatures between 40 and 125 degrees F. ( 5 and 52 degrees C )

Using the "degree" symbol seems correct, but in a range should it be specified for each? Do Fahrenheit and Celsius have the same symbol?

40º - 125º F, 5º - 52º C

Both Fahrenheit and Celsius use the same symbol, just as they both use the same word. (In contrast, the Celsius absolute counterpart, Kelvin, omits "degree" or the symbol entirely.)

As for how often to use the degree symbol, you should use it in the same places you would spell out the word "degree" (or "degrees"), i.e. immediately preceding "Celsius" or "C" or "Fahrenheit" or "F", not following each number.

The biggest problem I see with your original wording is use of the verb "do". "Thrive" might be a better choice. Definitely nothing wrong with the way the temperature range is expressed.

When using the degree symbol in expressing a range of temperatures in Celsius or Fahrenheit, both numbers in the range can have the symbol, thus:

Water is as a liquid within the 32º – 212º F range • Last week's temperature range was 25º – 32º C.

In most scientific contexts, the degree Celsius (ºC) and the degree Fahrenheit (ºF) are units in their own right. Thus, I could rewrite the above examples thus:

Water is as a liquid within the 32 – 212 ºF range • Last week's temperature range was 25 – 32 ºC.

However, we only say degree after the both numbers in the range. Hence, when degree is written in words, it comes only after the range. I must mention, though, that this is strictly in a range defined with to. If and is used, then, strictly speaking, degree should be written after each number. Usually, Fahrenheit and Celsius are usually written out in full in this case, for consistency's sake. Thus, to use your first example, here are different ways you could write this:

• ... they do best in temperatures between 40 degrees and 125 degrees Fahrenheit (5 degrees and 52 degrees Celsius).
• ... they do best in temperatures between 40º and 125º Fahrenheit (5º and 52º Celsius).
• ... they do best in temperatures within 40 to 125 degrees Fahrenheit (5 to 52 degrees Celsius).
• ... they do best in temperatures from 40 degrees to 125 degrees Fahrenheit (5 degrees to 52 degrees Celsius).
• ... they do best in temperatures from 40º to 125º Fahrenheit (5º to 52º Celsius).

Truth be told, authors abide by various conventions in different contexts. I will illustrate the possibilities:

• 20 – 100 ºC
• 20 ºC – 100 ºC
• 20 – 100 (º C)
• 20 – 100 (º Celsius)
• 20 to 100 degrees C
• 20 to 100 degrees Celsius
• 20 degrees and 100 degrees C
• 20 degrees and 100 degrees Celsius
• 20º and/to 100º C
• 20º and/to 100º Celsius
• 20º – 100º C
• 20º C – 100º C
• 20º – 100º Celsius

Finally, the degree symbol is the same, whether you are on the Celsius or Fahrenheit scale. In fact, there is no other degree symbol. So, there is no choice. For the Kelvin scale, the degree symbol is never used (although some erroneously do so). Hence:

293 to 373 K • 293 to 373 kelvin • 293 – 373 K • between 293 K and 373 K, etc

I prefer (and have seen it this way in most of my engineering textbooks):

(...) they do best in temperatures from 40°F to 125°F (5°C to 52°C).

From my physics textbook, Physics for Scientists and Engineers by Serway and Jewett:

Explain how its energy output in one such time interval compares with the energy required to make a pot of tea by warming 0.800 kg of water from 20.0°C to 100°C.

From Molecular Thermodynamics of Fluid-Phase Equilibria (the first result for "thermodynamics" on safaribooksonline.com):

If mercury were heated from 0°C to 1°C in a constant-volume system, (...)

In order to eliminate the awkwardness of the parenthetical, I'd recommend either:

They do best in temperatures from 40º - 125º F (5º - 52º C).

or

They do best in temperatures between 40º and 125º F (between 5º and 52º C).

I'm hard-pressed to explain why the "between" needs to be repeated inside the parentheses, but to me it looks very awkward without it and quite reasonable with it.