The problem with wood burning stoves is the particulates (microscopic fragments of wood and ash) emitted into the atmosphere with the flu gases. However modern stoves and flues are designed so that particulate emissions are minmised and the standards for moisture content in fire wood means that all wood sold as fire wood must meet these standards when sold. When delivered firewood should be stored under cover
We have a woodburner in our house in England and our holiday home in France. Both are modern stoves with approved flues to match, one was installed only three months ago and in one case the wood is stored in an open ended barn attached to the house and the other in one end of a big garden shed.
My concern Katek would be about where you want to install your stove. How big is your sunroom and what are the walls and ceilings made from? I would be very wary of installing a wood burning stove in a sunroom where the ceiling or walls were made of plastic or where the room was smaller than about 8 ft x 10ft. Even the smallest stove can have a large heat output and unless the sunroom has a built in brick chimney I would be concerned about the siting of the flu and the danger to a plastic roof.
A wood burning stove does not seem to me to be either a safe nor aappropriate way to heat a sun room.
Analternative is a heater using bottled gas, calor or similar. They are attractive in design, and portable and just require a bottle of gas appliances.calor.co.uk/ and would be more suitable for occasional use in a room of the kind the word 'sunroom' conjures up for me.