A Milton house fire that killed a prominent Boston ­developer and his father-in-law began when a space heater overloaded an extension cord, investigators said Tuesday.

The electrical fire began just after midnight on Monday in a second-floor bedroom, where two oil-filled space heaters were in use, officials said.

One was plugged into a power strip and the other into an extension cord. Neither the strip nor the cord was ­designed to carry the electrical load drawn by a heater, according to a statement from State Fire Marshal Peter J. ­Ostroskey and Milton Fire Chief John Grant.

“The electrical fire started where the extension cord and the space heater were connected,’’ the officials said.

Kenneth Guscott, 91, a developer who was instrumental in the revival of Dudley Square, died in the fire, along with his father-in-law, Leroy Whitmore, 87. Guscott’s wife, Valerie, and their teenage son, Kenneth Jr., told firefighters the two men were trapped inside.

Ostroskey said the fire on Elias Lane is an example of the dangers of using space heaters without the necessary precautions.

Though space heater fires are not common, Ostroskey said one out of every 15 fires linked to the appliances causes a fatality.

“Older adults often have a harder time staying warm in the winter. As we help our seniors keep warm and keep safe, it is important to plug space heaters directly in the wall outlet and keep them three feet from anything that can catch fire,’’ the fire marshal said in a statement.

Chief Grant noted that the home had working smoke alarms and that the fire does not appear suspicious.

“This fire was a tragic loss not only for the family but for the greater Boston community. The fact that the home had working smoke alarms prevented this tragedy from being any worse,’’ the chief said.

Andy Rosen can be reached at andrew.rosen@globe.com. Follow him on Twitter at @andyrosen.