Ratings for rooms don't map well onto greenhouses, because they don't expect a room to be all windows
If you have something like that professionally "sized" you'd end up with a MUCH larger unit than for a "normal", insulated room. Typically, greenhouses have entire wet-walls for cooling, with surprisingly massive fans driving the system.
The units I've seen (greenhouse coolers) use swimming pool type pumps which incorporate air cooling (built in fan that pushes air over heatsink fins on the body) - they are capable of continuous operation. Never seen a "domestic" "swamp cooler" so not sure what these use; they ought to have something capable of 24/7 operation in them, but I guess some people cut corners...
---------- Post added at 10:33 AM ---------- Previous post was at 10:30 AM ----------
Thermostats are basically the same as timers - automated switches. You could quite easily swap them out more or less part for part; if you're worried about installation, any competent electrician could swap them out in moments.
The only two complications you might find are the rated current and voltage; if these don't match, you either need a different unit or to install a relay.
Incidentally, if you want to retain time control, there's no reason you can't put the thermostat in circuit after the timer, but be aware the timer will "win" in any decision-making wrt being off (and the thermostat likely the opposite). Wired in parallel, both can "choose", but you lose absolute time control; I wouldn't recommend this configuration. I have one circuit that drives lights that has both timer and light sensor control; using a relay, I've reversed the output of the "turns on at night" light sensor to turn the circuit off at night; the timer gives me additional control if I want it (mainly, I use it to turn the lights of for 15/60 minutes as the ballast doesn't seem to like continuous operation). It was an annoyingly expensive ballast and has never worked right (a
Hagen "glo" t5 model; the right size for the tubes I'm using).
If I owned the building I live in, I would long ago have installed an "exhaust" fan that turns on if my humidity gets too high, or the temperature too extreme (with some kind of circuit to not do that if the external temperature is even hotter, which happens; it can get to in excess of 45C here on a bad day).