They were unsympathetic — and arrested him Monday.

He faces a third-degree felony charge of sexual misconduct with a detainee or offender.

”Any sexual contact is an abuse of authority,” said Miami-Dade State Attorney Katherine Fernández Rundle.

Coronado, 34, was linked to the December 2005 episode at the Homestead Correctional Institution by DNA from the woman’s panties, says the Florida Department of Law Enforcement.

The guard, agents say, had an illicit, one-afternoon stand with a career criminal imprisoned for forgery, grant theft and burglary.

The woman told agents she had been ”playing around” with Coronado to get him busted for bad behavior. Flirting, she stole his pen on Dec. 30, 2005, proclaiming it hers.

After other inmates left for lunch, Coronado demanded to see what was in her locker, agents say.

The rest of the rendezvous detailed in the arrest affidavit, which lasted ”between 30 seconds to a minute,” describes the sexual encounter.

She first told her story to prison inspectors Cary Ryan and George Montenegro in January 2006. Three days later, she gave a sworn statement to FDLE agents Jeremy Rosenthal and Edward Royal. She also gave them underwear she said she wore during the encounter.

At first, agents say, Coronado denied he had sex with the woman. He did, however, volunteer a DNA swab.

The results from that DNA test came back in November.

Later, he admitted he had sex with her, but only after she ”made sexual advances at him on a daily basis for approximately one month.” The FDLE didn’t say why it took four months to arrest Coronado.