Covering the floor with dark pavers/blocks set in sand would be a good idea. No worries about rot or harboring pests, and it would increase the thermal mass heated by sunlight. Rather than blowing hot air from a single source, I bought a patio heater with three quartz radiants and rewired them to a thermostat, to heat the foliage directly.
Going on 12 years with no problems (except bugs).
