[Gretl-users] [OT] Including combined dummy-variables

Hello, sorry for posting such a probably off-topic question to this list but I don't know of any other place I could ask. I am fitting an arima model with exogenous variables and was trying to identify if there exist differences between the relationship depending on the season of the year. Therefore I added a combined Variable which combines a binary dummy for the season (Summer, Fall, Winter) with the exogenous variable the logarithmic average temperature on a particular day. So I have three Dummies (LogAvgTemp x Summer, ..., LogAvgTemp x Winter). Now I don't know if it's sufficient if I add those three combined dummies or if I should also add the LogAvgTemp as an additional exogenous variable. Perhaps someone could point me to a text book or something similar which might address such a problem. Thanks in advance and once again sorry for being slightly off-topic, johannes