ASTM E10 only requires that the manufacturer of calibration blocks perform the calibration at 23+5oC.
As long as the calibration blocks & material being tested are similar material & at the same temperature, any ambient temperature comfortable to the operator should be OK. However, if not using calibration blocks, some of the force calibration methods as given in ASTM E4 require ~constant temperature (+2oF or +1oC).
The testing temperature range mentioned by yates is also found in ASTM E18 (Rockwell hardness testing).