Keith E. Stanovich and Richard F. West in their research paper on the relationship between IQ and common thinking biases emphasize that:

...for a given task, the mindware is available to carry out override (whether the procedures and declarative knowledge are available to substitute an analytic response for a heuristic one). If the relevant mindware is not available, then the person must, of necessity, respond heuristically. It is immaterial whether the person detects the necessity for override or has the capacity to sustain override if the normatively appropriate response is simply not available. If the relevant mindware (probabilistic thinking skills, falsifiability tendencies, disposition to search for alternative explanations, sensitivity to contradiction, etc.) is not present, then participants will end up at what has been termed in the figure Path 1 to a heuristic response.

 In other words, if the problem-solver doesn't know rational methods to solve a problem (mindware), neither his/her general intelligence, nor the awareness of the bias, are going to help come up with a good solution.

Journal of Personality and Social Psychology, 2008, Vol. 94, No. 4, 672–695
( reference to the paper from marginalrevolution.com)