Step 1: General concept.
Silicon in hot metal mainly comes from reduction of silica in coke ash. This reduction is more favorable at high temperatures. To reduce silicon pickup, the process should reduce the effective high temperature and capture silica before it enters the hot metal.
Step 2: Check each option.
- (A) Reduced flame temperature decreases silica reduction. Correct.
- (B) Oxygen enrichment improves efficiency and lowers coke rate. This shortens the high temperature zone and reduces silicon. Correct.
- (C) Lime injection increases basicity and captures silica as slag, preventing its entry into hot metal. Correct.
- (D) Increased hearth temperature promotes more silicon dissolution, which is unfavorable. Wrong.
Step 3: Conclusion.
The favorable conditions are (A), (B), and (C).
\[
\boxed{\text{Correct: (A), (B), and (C)}}
\]