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Will the fumes from indoor heaters that run on propane gas be harmful to turtles? I don't want to use the heaters if they'll be a danger to my little ones.

How close are the heaters to the turtles? If the fumes are as strong as you seem to suggest, I don't think they're safe for humans either...

Is the indoor heater properly vented to the outside? If not you are risking a fatal buildup of carbon monoxide levels that will kill any inhabitants inside including turtles and other animals. If it's a portable type propane heater is should not be used in an enclosed space. There should be a warning label on it stating that. You hear about people dying from using those indoors every winter during power outages. Carbon monoxide is both odorless and colorless and can build up to lethal levels without you even noticing it. Usually by the time you notice the effects, it's too late (you pass out).