Walter Powley suffered serious burns following a fall at the Western Park View home in Hinckley Road, Leicester, in May 2012.
An investigation into his death found the radiator pipes and valves at the home were not covered.
It also found the owner was aware that Mr Powley was at risk of falls.
During a hearing at Leicester Crown Court, Western Park Leicester, based in Queen Street, Wolverhampton, pleaded guilty to safety breaches.
The firm was also ordered to pay £35,000 in costs.
In a statement, the Health and Safety Executive (HSE) said Mr Powley had been admitted to the home four days before being injured.
It said he fell in his room and suffered serious burns to his right leg from the radiator pipe and valves, and superficial burns to both legs.
He died in hospital eight days later.
Speaking after the hearing, HSE inspector Dr Richenda Dixon said: "This was a foreseeable and preventable fatal incident.
"The scalding or burning risks from the pipes were long-standing and could have caused injury to any resident," he said.
In a statement on behalf of Mr Powley's family, his son Colin said: "We are still devastated, not only by our dad's death, but also how it came about.
"The fact that he died from injuries sustained as a result of, in our view, inadequate care in a place where he was supposedly safer than at home, is heart-breaking."
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