First Time Lotl Mama--lowering temperature?

Hey there, I'm a first time axolotl keeper. I haven't gotten my lotl yet, I'm letting the tank cycle right now, but the temperature worries me. It's about 86 degrees, meaning I've got a hell of a lot of a ways to go until its satisfactory. The tank I'm using right now is 10 gallons, but when my lotl gets bigger, I'm going to move her to a bigger tank.
I keep my ceiling fan on and when it's cold out I open my window, but regardless, I can't get the temperature low enough. It worries me because right now it's Winter in Texas, and the temperature is around 40 degrees outside, but in summer it can easily get over 104 degrees.
My room temperature is relatively low as well, I think around 65 degrees and that's about as low as I can get it.
I guess it's worth noting that I'm using a strip thermometer, which I've heard are much less accurate? I'm going to replace it ASAP but I doubt it's a whole 26 degrees off hah.
Thank you!

What kind of lighting do you use? Do you have a lid on your tank, what kind? The tank temperature shouldn't be that high if your room temperature is only 65F unless there is something heating the water.

No lighting, no cover. I'll probably end up getting a mesh cover before I get my lotl.
Here's a picture. The room is a little darker than it usually is as it's early morning and I'm on my way out the door but the temperature remains the same.

Does the water feel that warm? I would double check with a second thermometer. The only thing I can think of is the filter pump running way too hot, and even that seems a stretch to add that much heat. You can get a floating thermometer to double check for around $2.99 or so.

Is the strip inside the tank or are my eyes just weird? It should be on the outside and is probably broken if it's in the water.

I live in New Mexico and summers here are brutal as well, the easiest way I have found cooling my tanks is to place a box fan over the top of the tank. It doesn't create much water movement and it keeps the tank at least 5-10 degrees cooler.

Does the water feel cool to the touch? Sometimes those thermometers can be off, and like everyone else has suggested, you might want to get a second opinion (thermometer)

You can also create ice cubes out of the tank water, and throw them in for a quick cool off if need be. Some users will also freeze water bottles to let float on top.

Hey, just so you know, I got it figured out. I bought a new aquarium thermometer (the old school suction-cup-and-mercury-kind) and as it turns out the temperature is actually under 70 degrees. Let this be a warning to all that strip thermometers do not accurate readings make. ^^ At the very least I know my lotl'll be happy with it!