OMG, a 7mm wetsuit in tropical waters? I'm gasping just thinking about it.
We were diving a shallow dive in 64*F water off Catalina last month in our 7mm wetsuits/hood/gloves. There was a class finishing their OW certs so my wife and I jumped off the boat and took a little tour. My wife was comfortable and I was sweating, pulling at my neck letting water into the suit.
On the next dive we moved to a pinnacle less than a mile offshore. Expecting the same temps, I removed my gloves. Turns out the water was 56*F and I needed my gloves, but at least I was not sweating. My ungloved hands make good radiators if I'm overheating.
We wear 3mm wetsuits in 75-81*F Carribean water, no hood. 81 is about my maximum for the 3mm. Beyond that I'm in a skin, or a skin and shortie if doing three or more consecutive dives.
You can always buy a polypro dive skin (1mm equivalent) and a tropical hood to add to the 3mm if you feel the 3mm is not enough on your 2nd and 3rd dives. A hood make a huge difference.