Excellent point a very timely. Any time your shop is at a low temperature for a period of time, your tools acquire the same temperature. When you turn on heat, the air will heat up faster than the heavy pieces of metal or cast iron. This creates a small local environment within a close distance from the colder surface. This environment is moisture laden and you will end up with water condensation on the metal. This is the reason that tooling rusts.
The solution is to keep the heat on all the time or to do something to cause the tooling to heat up faster. Some use a blanket over the tool with a 60-100 watt bulb lit. I find that just using one of the cheap Walmart "Throw Blankets" that cost a few bucks works very well. Just be sure that the blanket is in contact with the surface.
On a related note, be very careful with open flame heaters in a shop. Combustion of dust is only a very remote possibility. More dangerous is carbon monoxide poisoning. My recommendation is to only use an external vented device and to mount a CO detector in your shop.