I agree with Dan. Ultimately, it is the vapor pressure of the repellent compound that dictates the temperature need to volatilize it. Some solids and liquids have have enough vapor pressure at ambient temperature to be effective without heating. Consider naphthalene in old-style moth balls and moth flakes (which can still be purchased outside of California) – they slowly sublime from a white crystalline solid to a vapor at room temperature.
But a compound with a lower vapor pressure would need to heated or aerosolized in some way, perhaps through ultrasonic vibrations, but that too, would take some energy.
Reviews on the brand I pulled up indicated each butane cartridge lasts 12 hours. The little repellent pads, about 4 hours each.
If you used the liquid without any heat, there might be some amount of surface area that would evaporate enough of the compound to work. You could try smearing it over a larger piece of paper or plastic wrap or waxed paper and see if it’s effective at reducing mosquitos.
It appears to get the repellent pads pretty hot because they appear somewhat singed after use. If it does have to get over 350F, there might not be any surface area at 70F that would be adequate. Maybe a flexible Fresnel lens rolled up, and then deployed aimed at the repellent pad? But it would only work during daylight an carry some risk of lighting the picnic table on fire.
Seems to me that burning mosquitos coils is a more direct approach and leaves you with nothing to carry out if you’ve provisioned perfectly.