Competence in one domain translating into a subjective perception of competence in an unrelated domain

The "halo effect" is defined by oxforddictionaries.com as

The tendency for an impression created in one area to influence opinion in another area

Usually, this term would be applied to the opinions of others towards the would-be cross-disciplinary expert described the question, but perhaps it could be applied to the would-be expert's opinion of him- or herself.

Appeal to Authority (argumentum ad verecundiam or argument from respect). A logic fallacy wherein a reference is made to an established authority in one field in support of an opinion in unrelated subject. The established authority can be the reputation of ones own self.