For a Don Fogg style drum furnace, you'll probably do best with a Mineral-Insulated type K thermocouple, of 6mm or 1/4" diameter. Suitable sheath materials are Inconel, 310 stainless steel (which is what I use) or maybe Omega's "Super Omegaclad XL" if you are feeling flush and/or intend to treat stainless steels.
The Mineral Insulated assembly, at 6mm dia, is rigid enough that you can profile the temperature over the full length of the chamber to confirm it is even enough for your purposes. You can then put the tip in the best place for actual Heat Treating. You'll need the MI assembly to be long enough to reach the full length, plus enough that the hand holding it has enough to grip and doesn't get burned when it's at the back: maybe 48" long? It's best/easiest to get a transition probe with a miniature connector to suit a handheld digital readout. That way the supplier deals with the wiring and you don't need to worry about it (it's not difficult to wire thermocouples, but it needs the correct wire and connectors and it needs to be done correctly. It's usually cheaper and invariably easier to get the thermocouples complete with fitted leads and connectors).
Cheap pyrometers off ebay are plenty good enough. I used TM902Cs for years (degC only, but around 6-7 bucks delivered and they come with a glass-fibre insulated bead probe that is about 3 ft long, good to about 400 degC (750 degF) and perfect for checking the temperature of whatever you use for tempering: it'll close in the domestic oven doorseal, for example. I have access to a calibrator and stopped using/recommending the TM902Cs when I got a bad batch of them a few years ago. The bad ones were very accurate to 800 degC, but then started to deviate at higher temperatures: I can't remember whether they read 1290 degC at 1372 degC, or read 1372 degC at 1290 degC. Even the bad ones are fine for Carbon Steel HT temperatures, but they are no good if you want to check a forge is running at welding temperature. I've been using mostly 6802 pyrometers since: boringly accurate when tested against the calibrator, display degC or degF, and cost around 25-30 bucks delivered. It seems to be a bit of a lottery whether they come with the Glass-Fibre insulated probe, or a PVC insulated probe which is much less useful to us.
The biggest supplier is probably Omega. They are not cheap, but they are not silly-expensive either. If you use them, I would recommend sitting down with a cup of coffee and a notepad, listing your requirements and calling their technical sales line. They know their stuff and you'll learn something if you listen to their advice. Other thermocouple suppliers are out there. I'm in the UK and could list several over here, but can't help with US-based suppliers.
