I'm guessing that if it's a kiln, you're running type R or S T/C's made of platinum elements and expensive at current noble metal prices?
The comments on high limits can not be ignored, especially for a high temp kiln, which can be a fire hazard.
The lack of T/C break (burnout protection) can be a serious issue for the control T/C, as well.
Do any of your devices have universal analog inputs that can be field configured for either T/C or 4-20mA (might have to add a shunt resistor for 4-20)?
The Omega OMNI-AMP IV cited above appears to be mV amplifier, not necessarily a mV follower. The Gotcha is the statement:
Please note that the amplifier has cold junction compensation but not linearization.
The spec sheet statement that the output is either 10mV or 1mV per degree F (depending on input type) is somewhat deceptive, because without linearization X mV/Deg is a merely an approximation.
The schematic in the user manual
http://www.omega.com/manuals/manualpdf/M2074.pdf
confirms that, showing the CJC compensation, along with the amp, no linearization.
It isn't clear whether the amp can run at a gain of 1 which you'd want if you expected to make no other changes in your existing system. If run at higher gains, the lack of linearization puts the burden for linearization on the receiver device, which is what is already built into T/C inputs. To have to linearize a mV input to T/C curves is lot of work to set up.
With a spec sheet statement: 1mV per Deg F
a gain of 1 is questionable.
a 1mV difference for a Type R T/C at 2000°F is
131° difference (on the high side) 2,000 to 2,131
134° difference (on the low side) 1,866 to 2,000
1,866°F = 10.757mV
2,000°F = 11.759mV
2,131°F = 12.758mV
type R °F tables at
http://www.pyromation.com/downloads/data/emfr_f.pdf
The calculation of the gain needed for a specific 'range' is rather cryptic, without a generic formula to follow.
Is the range 0 - 5.0 V below 32 to 532°F or 0 to 500°F?
Look in a table on the thermocouple to be used for the thermocouple voltage at the
temperature of interest.
A type K has an output of 11.289 mV at 532°F, i.e. 500°F above 32°F.
The gain required is 5.000V/.011289 = 442.9.
You can then apply .010 Volts to the amplifier inputs and adjust the gain for an output between pins 1 and 2 of 4.429 Volts, or apply 11.289 mV and adjust for an output of 5.000 Volts.
Remove the ******t output jumper and connect up the thermocouple.
You might want to figure out how you'd use it before you actually jump in the deep end.
Dan