IPA: /ɪnˈsɛnseɪtli/
KK: /ɪnˈsɛnseɪtli/
In a way that shows a lack of feeling or understanding; without awareness or sensitivity.
He insensately ignored the warnings about the storm and went out anyway.
Insensately is formed from "in-" (meaning not) and "sensate" (from Latin "sensatus", meaning having sense or feeling) and the suffix "-ly" (meaning in a manner). The word describes an action done in a manner that lacks sense or feeling, hence thoughtless or irrational behavior.
Think of 'not having sense' ('in-' means not, and 'sensate' relates to feeling) to remember that 'insensately' means acting without thought or feeling.