Is a temperature of -70° C less or more than -80° C? I ask because of something I read in a news story about the mountain range under the Antarctic ice sheets. The story reads, “Conditions are brutal; temperatures can go down to more than -80° C.”

Could they go down to -85°C? (Yes.) Then would not that be less hot than -80°C, and, therefore, should not that sentence read “temperatures can go down to less than -80°C”?
How about lower and higher. Temperature can go lower than -85
Yes, lower would work. Technically, a temperature measurement measures heat energy; so below 0 degrees Celsius, “less than” or “lower than” would be appropriate.
If you’re reading the sentence as “More than eighty degrees below zero,” it would make sense, as “more than” references “eighty,” not “below.” The real problem in the sentence is that “temperatures can go down to” indicates a fixed point, where “more than” is obviously flexible, so the statement is meaningless. (See the common “Up to 80% off and more!” for reference.)