IIRC the ASOS reports in degF. However it's all distributed in the hourly METARs, special obs, and 5-min obs in degC.
The problem is there is a different between the coded obs sent out in the hourly METARs and the ones for the 5min obs. The hourly METARs have a "T" grouping in the remarks that reports the temperature in tenths of a degC so that the precise conversion to whole degF can be made. Hence, 35.6C (96F) and 36.1C (97F). Basically take any reasonable whole number temp in degF and convert it to degC and round it to the nearest tenth to see what the opssible values are in the remarks section.
For example...
93F = 33.9C
94F = 34.4C
95F = 35.0C
96F = 35.6C
97F = 36.1C
You won't see 34.1C or 35.1C or 35.7C, etc in the remarks because it doesn't convert to a whole number in degF.
As for the 5min obs, all they report is the body of the coded observation and no remarks. So all you're left with is the rounded value. So you could see the :50 5-min ob be 36C (96.8F), the hourly :52 METAR 35.6C (96F), and then the :55 5-min 36C (96.8F), but in actuality they may just all be 96F. That's basically what happened with CAR today.
So take 5 1-min raw observations...
:01 93F
:02 95F
:03 94F
:04 94F
:05 93F
The official ob for :05 would be 94F since it's a 5-min running mean. If it was an hourly METAR it would get reported in the remarks as 34.4C which convert to the nice, easy rounded value of 94F. If it was a 5-min ob, only the body gets reported so the temperature gets disseminated as 34C. Websites convert that to degF which would be 93.2F even though the real actual temperature is 94F.
What we need is for the NWS/NOAA to just give us the T remarks in all observations to avoid this issue. It's not 1996 anymore...we don't need to worry about bandwidth and writing AFDs in abbreviations anymore.