Yes, you can.
Isn’t trivial but not too bad.
Basically take apart the little control unit in the front.
You want to “unplug” the power going into the unit from where it plugs into the board.
To do so you have to practically unplug everything because they’re stuck in there pretty good.
Then take some 12ga wire [ex: normal romex].
Cut some little pieces of it, strip both ends.
Use those to “connect” from the power to the outgoing “high” or “low” connector piece, and the outgoing pump wire. connector Then cover those with electric tape.
Plug everything else that’s not “now hot wired” back into the board (basically just to connect their “white common” wires back to the incoming “white common” wire, through the board, but it’s convenient to do it this way).
Put cover back on.
Now just plug it into an “outlet thermostat” that you can buy on amazon.
Put it all back together, it actually fits in the box still if your new wires are short enough.
Basically at this point it’s hard wired, if it’s getting any power “into it” it will be on.
Drawbacks: you can’t easily switch from “high” to “low”.
But you can still control it by unplugging it if desired.
Benefits: you don’t have to manually turn it off (ex: after going to bed). It’ll turn on and off as needed to reach the temperatures you want while you sleep.
And when you go on errands.
It keeps it at a stable temperature during the day when you’re awake, too.
Pro: since it’s pretty non damaging, you can revert back to the remote way.
Thought: you might be able to replace the entire front grille with the “non remote” version and get the same effect. At greater cost. Haven’t tried it yet though…
More details available upon request leave a comment below.
If you want to get a lot more invasive you could cut its wires and then join them to wires coming out of some “wall evap. cooler thermostat” then it would control both high and low.
I’m OK with just low in my case, YMMV.