I had to deal with my short queen back when I bought my trailer in 2005. But to answer your questions...
Personally I wouldn't be too concerned about the vent. At least in my trailer I can stand in bare feet on any of the vents and never feel more than warm air coming out. Meaning I've never had the temperature get anywhere near uncomfortable much less hot.
As far as putting a full size mattress on it you could easily just add a mattress to the existing base and it will probably be fine. But do you have to lift the bed to access storage underneath? If so you're going to have to put some stronger lift supports under the bed to be able to compensate for the longer and heavier mattress. On my short queen with a foam mattress topper and a sleeping bag or two the bed would barely stay lifted. I had to do some research off the labels on the supports to find they were 100lb supports. I upgraded to 120lb supports and now the bed works a lot easier and stays up with the bedding on it.
Here's what I did on my trailer. Granted it's not for everyone but it works for me. I added PVC legs to the solution because the person on the other side of the bed typically tries to go around the feet of the person blocking them for a bathroom break in the middle of the night. I didn't want to take a chance of the mattress flexing in the middle of the night and a knee or leg slipping off through the gap.
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