For what you're looking to do, you don't really need to buy a thermometer, you could simply Buy one of the cheapy temp controllers and use that. Obviously you're not going to need the output, although it does have that so if you wanted it there you go. The ones available on eBay are only a couple of bucks and they use a standard thermocouple which of course there are different types, but you're typically going to use a k-type and from there all you need to do is purchase the one you want. They make them anywhere from a half inch long to a couple feet.
Here's one that comes with a solid state relay and the thermocouple for 20 bucks. Now you would need to replace the thermocouple most likely because you want a long probe. This one is as it says a k-type. Simply purchase another k-type of a different shape. That you'll have to find separately but you can just look on ebay. The k-type just represents the temperature range and the output.
https://www.ebay.com/itm/REX-C100-D...r-Set-K-Thermocouple-Max-40A-SSR/175311089284
The thermocouples have Spade connectors that connect to screw terminals on the back of that PID controller. I don't know if it's absolutely a fact but you probably want to use Spade connectors that they put on at the factory rather than Mickey Mouse'n one together. The entire premise of a thermocouple is such that you really want to make as few connections as possible with anything of your own. Remember they work by measuring the voltage between two pieces of metal. I don't mean they put a voltage across, I mean two pieces of metal that touch generate voltage and they measure that. It ain't much electricity. So you don't want to make unnecessary connections that will alter that voltage.
Hth
