A lamp can certainly give you both the hotspot and ambient temps your snake needs. You are going to need either a desk lamp or a lamp stand so the heat lamp is not rested on the tub as that will melt the lid.
I really like these lamp stands as they are extremely adjustable and sturdy.
https://www.amazon.com/Zoo-Med-Repti...med+lamp+stand
Im not sure the tstat you have will work well with the lamp though. It is a on/off tstat vs. a proportional version. This would make the lamp turn off and on as the temp needs adjusting which will probably burn the light out quicker if it works at all.
You may need to visit a hardware store and pick up a rheostat(dimmer). They are not ideal but you need something to control the lamp.
https://www.amazon.com/Lutron-TT-300...words=rheostat
If you were to get the lamp stand you could also use it to control the heat by raising and lowering the lamp until you get the temps you need. To make the hotspot warmer you would lower the lamp toward the tub and the lower the temp you would simply raise it.
Both a dimmer and lamp stand adjustment will work best if your home does not fluctuate much during the day and night in its inside temp.
Placing the uth under the tub should still work fine though and I would get that set up now so the snake can at least have a good hotspot top lay on.
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