Dont worry about a portable space heater they usually just push warm dry air that is very dry. Any lighting would provide some added heat even under lights you'll still need to move the drying heat by way of fan.

Keep in mind plants dont grow in just dry heat thats also provided by lighting, the only thing heat does is cook.

Moving air by way of fan will allow them to breath and help prevent them deceptive lack of moving air wrinkles that appear to need water when what they also need is a cooling air and maybe water

Where ever zone none is if you able to plant in ground any of them or cold frame I suggest you should

Here is a link that might be useful: This should help

I live in Houston so could I get a space heater And a fan?