The answer to this issue depends on whether you consider your room to be a three-season or four season environment. As it should be evident, there really is a big difference between them. A three-season sunroom does not have to retain heat as efficiently as a four-season garden room for the simple reason that it will not be used as much in the winter. So for this kind of sun room, you may not need any supplemental heating if you live in the southern climes. Simply having a lot of sunlight streaming in is probably enough.
During the summer, you may have the problem of your three-season room being too hot, so it is strongly advised that you install at least one ceiling fan. For a four-season sunroom, there are several options for heating. First, you could have the room open to your main living space, and just place that additional load onto your heating system, whatever that may be. Secondly, you could install some low-maintenance baseboard electric heaters, which provide nice supplemental heat without a new heating system.
If the space is really big, you may have to add additional tonnage to your current HVAC system. This also applies to air conditioning options. Again, it is strongly recommended that you have at least one ceiling fan in your four-season sunroom for heat circulation (remember to reverse the direction so the fan pushes the hotter air down during the winter, and pulls up cool air during the warm months).