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Abstract Conditions for anti-Unruh effect in (1+1)-dimensional spacetime are obtained. For detectors with Gaussian switching functions, the analytical results are similar to previous ones, indicating that anti-Unruh effect occurs when the energy gap matches the characteristic time scale. However, this conclusion does not hold for detectors with square wave switching functions, in which case the condition turns out to depend on both the energy gap and the characteristic time scale in some nontrivial way. We also show analytically that there is no anti-Unruh effect for detectors with Gaussian switching functions in (3+1)-dimensional spacetime.