Look up Pro Products radiant heat panels and give them a call. They will ask you all the relevant questions and recommend a panel wattage and size.
I personally use plastic cages that are very similar in size to the animal plastics T8 in conjunction with RHPs from Pro Products. They work well for me, however my ambient room temperature is a fair bit higher (~72 degrees F). I do not use heat tape with RHPs and I place the probe just below my heat panel. Radiant heat panels do indeed raise ambient temperatures, but the amount is highly variable. RHPs do not heat air, they heat objects within the cage. The objects then give off heat to the environment. The amount the RHP raises the temperature thus depends on the objects within the cage and the cage itself. For example, mine raise the ambient from around 72 degrees F to around 79-80 degrees F. My panels are the P3 model and are (I believe) 65 watts.
I do not know if an RHP can raise the temperature from 65 without heating the panel to an unsafe level, but Bob at Pro Products should be able to answer that question.