The CAS/Mach No relationship is independent of temperature. However, the TAS/Mach No relationship depends ONLY on temperature. This confuses people.
Most pilots are only interested in the TAS/Mach No relationship. On most aircraft you use your CAS to determine TAS up to a certain altitude, then use the Machmeter beyond that altitude. So, in general, you're not terribly interested in the relationship between CAS and Mach No, because you don't need to use it. Again, on most aircraft which operate above or near the tropopause (ie, most airline medium to big jets), you climb using an initial CAS until you hit a certain Mach No, then continue the climb by holding the Mach No (I know that lots of you will write in with examples of aircraft which are the exception, but, nevertheless, it's a pretty general rule).
Because of the temperature range you actually practically encounter in realistic atmospheres, Mach 1 is nearly always between about 550 and 650 knots TAS. At around 30 - 35000 feet, it's nearly always very close to about 600 knots.
This means that, provided the head/tailwind component is fairly small in comparison to your TAS, the Machmeter becomes a mile-a-minute meter. Suppose you're at M 0.8 and you've got a head/tailwind component of 20 knots or so. You can disregard that for all practical purposes compared with your TAS of about 480 knots. 480 knots is 8 miles a minute. Mach 0.7 is 420 knots. That's 7 miles a minute. Mach 0.6 is 360 knots. That's 6 miles a minute - and so on.
So, if you're doing M0.7 and the DME shows 77 nm to the next reporting point, provided the wind's reasonably light, you've got 11 minutes to run - just like that!