Ultimaker Original temperature sensor replacement? The title almost says it all.

I was searching on websites like amazon.com and ebay.com for a replacement of the temperature sensor of my Ultimaker 1, but could only find replacements for Ultimaker 2 (PT100), but I know those aren't compatible.

What specifications have replacement temperature sensors that work with the tc2 signal amplifier of the Ultimaker Original?
You need a thermocouple, not a thermistor. Also, as you say the Ultimaker Original+, and the Ultimaker 2, (which both use version 2.x.x boards) use a PT1001.
According to this post, on E3D Thermocouple mount on UMO+, a k-type thermocouple will do:

I am changing over to E3D V6 on my UMO, and have elected to used the k-type thermocouples sold by e3d with the standard/original UMO amplifier board.

Or to be more precise, from this post, on
THERMOCOUPLE SENSOR REPLACEMENT, it is a 3 mm k-type thermocouple:

I would ask the reseller to measure the thermocouple to be really 3mm. I never bough a thermocoupler so no idea. I know that some aliexpress sellers did sell me a pt100 with 3.05mm (it doesn't fit in) so is good idea to ask for a photo with a caliper before paying.

The thermocouple in question, on AliExpress was this, SWMAKER Thermoelement Typ K (TC) für Ultimaker Original 3D drucker 3mm K thermoelement typ für Ultimaker Original 3D drucker, ~$10
Or this, considerably more expensive at €33, Ultimaker Original - Thermocouple Sensor (out of stock):


With respect to the firmware, from this post, on E3D Thermocouple mount on UMO+

Normally you won't have any modifications to do cause your UMO already works with a thermocouple.

So, assuming that you have an AD595 amplifier and not a MAX6675, ensure that you have
#define TEMP_SENSOR_0 -1

set in Configuration.h
//===========================================================================
//=============================Thermal Settings  ============================
//===========================================================================
//
//--NORMAL IS 4.7kohm PULLUP!-- 1kohm pullup can be used on hotend sensor, using correct resistor and table
//
//// Temperature sensor settings:
// -2 is thermocouple with MAX6675 (only for sensor 0)
// -1 is thermocouple with AD595
// 0 is not used
// 1 is 100k thermistor - best choice for EPCOS 100k (4.7k pullup)
// 2 is 200k thermistor - ATC Semitec 204GT-2 (4.7k pullup)
// 3 is Mendel-parts thermistor (4.7k pullup)
// 4 is 10k thermistor !! do not use it for a hotend. It gives bad resolution at high temp. !!
// 5 is 100K thermistor - ATC Semitec 104GT-2 (Used in ParCan &amp; J-Head) (4.7k pullup)
// 6 is 100k EPCOS - Not as accurate as table 1 (created using a fluke thermocouple) (4.7k pullup)
// 7 is 100k Honeywell thermistor 135-104LAG-J01 (4.7k pullup)
// 71 is 100k Honeywell thermistor 135-104LAF-J01 (4.7k pullup)
// 8 is 100k 0603 SMD Vishay NTCS0603E3104FXT (4.7k pullup)
// 9 is 100k GE Sensing AL03006-58.2K-97-G1 (4.7k pullup)
// 10 is 100k RS thermistor 198-961 (4.7k pullup)
// 11 is 100k beta 3950 1% thermistor (4.7k pullup)
// 12 is 100k 0603 SMD Vishay NTCS0603E3104FXT (4.7k pullup) (calibrated for Makibox hot bed)
// 13 is 100k Hisens 3950  1% up to 300°C for hotend &quot;Simple ONE &quot; &amp; &quot;Hotend &quot;All In ONE&quot; 
// 20 is the PT100 circuit found in the Ultimainboard V2.x
// 60 is 100k Maker's Tool Works Kapton Bed Thermistor beta=3950
//
//    1k ohm pullup tables - This is not normal, you would have to have changed out your 4.7k for 1k
//                          (but gives greater accuracy and more stable PID)
// 51 is 100k thermistor - EPCOS (1k pullup)
// 52 is 200k thermistor - ATC Semitec 204GT-2 (1k pullup)
// 55 is 100k thermistor - ATC Semitec 104GT-2 (Used in ParCan &amp; J-Head) (1k pullup)
//
// 1047 is Pt1000 with 4k7 pullup
// 1010 is Pt1000 with 1k pullup (non standard)
// 147 is Pt100 with 4k7 pullup
// 110 is Pt100 with 1k pullup (non standard)
#define TEMP_SENSOR_0 -1


However, according to
Questions about thermocouple and thermistor, the UMO board is 1.5.7, and can use NTC100K thermistors and (maybe - but it isn't clear) a 4.7K pullup resistor:

Firstly we have to do the Challenge with a Sainsmart UM Kit with that UM 1.5.7 Board.
We also have bought the print heads by E3D model V6 which have including ntc 100k thermistors which have already tables in marlin. As the V1.5.7. Board works with thermocouple, there was the question how to connect this. I got already an answere to just connect Signal and GND, to the board but I'd have to look for the resistors behind the connectors. Is it true, that I need a different resistor for each type of thermistor?

However, it is probably advisable to stick with the 3 mm k-type thermocouple, for simplicity's sake.

Footnote
1 Apparently for these reasons, from this post, on
THERMOCOUPLE SENSOR REPLACEMENT:

The UMO has the 'old' UltiBoard 1.5x which is a shield for an Arduino Mega, with the Pololu / Allegro stepper drivers plugged on it (Like the RAMPS controllers).
At that time RTDs where not very popular, and most printers came with thermistors. To improve the temperature feedback loop Ultimaker decided to use a thermocouple with an amplifier on top of the print head, which gives better results in particular at higher temperatures.
If you want to use a thermsitor instead of the thermcopule, you just have to swap the connections, and add a resistor on the board (the place for the resistor is foreseen on the board).
You can even go for an RTD using E3D's adapter plate.
The UMO+ is using the UltiBoard 2.x which is the same as in the Ultimaker 2, so it is PT100...

Note: RTD = Resistance Temperature Detector (such as a Pt100). A thermistor is similar to an RTD, but contains a ceramic or polymer resistor en lieu of metal.