For caloric testing, I am just thinking if we can do cold or warm water alone, why we need to do bithermal beside the benefit of better averaging.
Answer: Well your question already encapsulates one of the key reasons why one might need to perform all four irrigations (binaural & bithermal) i.e. that while mono-thermal screening reduces test time and predicts the bithermal result with high sensitivity and specificity but with certain criteria attached (e.g. the absence of spontaneous nystagmus and overall response size above a certain threshold).
The part about response size being above a certain threshold may be what you mean by “better averaging” – both monothermal results would need to be above a threshold in order to exclude bilateral canal paresis, otherwise the overall low figures could lead to a false positive.
Another reason to perform all four irrigations is measuring directional preponderance, which may give additional clinically relevant information.
You mention either cold or warm water alone – please do note that these concepts apply to both water irrigation and air insufflation (the other key method of caloric stimulation). You might also note that warm water (or air) stimulation is recommended as a mono-thermal caloric screening stimulus but cold water (or air) might be lead to lower accuracy in predicting the bithermal result (Lightfoot et al. 2008)
References and caveats
Lightfoot, G., Barker, F., Belcher, K., Kennedy, V., Nassar, G., and Tweedy, F. (2008) The derivation of optimum criteria for use in the monothermal caloric screening test. Ear Hear 30 (1), pages 54-62