Possibly ... depends a lot of the wattage of the bulb, the size of the box and if the temperature sensor is shielded from the direct heat of the bulb .
Using a relay might not be the best plan as you might need something to vary the heat output from the lamp
Most such projects end up with a bang-bang controller. If the temperature gets too low start heating, and if the temperature gets too high stop heating.
Tight temperature control is not easy to do with a relay.
You only need to replace the BTU lost so your heater should be selected to deliver heat as close to the amount that is lost.
The further you get from matching heat input to heat lost the more elaelaborate your controls need to be.
It would be wise to pulse the heater at a 50% duty cycle of 1 minute intervals and log the heat delivered.
Then repeat at 5 second intervals
Can you tell us your electronics, programming, arduino, hardware experience?
Thanks.. Tom...
I am so sorry . I didn't read these rules. I will be more careful next time . Thank you for your helps . I am student at Mechatronic Engineering and i have a little bit electronic experience.