Cold and low operation with N1 and ITT gauges only
 

CRJ200 for example has non FADEC engine and only N1, N2 and ITT gauges and is flat rated to 23 degrees C. If I operate from the airport where temperature is -20 and I accidently put 20 into the FMS for N1 thrust calculation will I get any information that something is wrong and engine parameters are exceeded during takeoff roll? As I understand N1 will stay in the green range ITT will be in a green range too but certified engine thrust rating will be exceeded without any cockpit indication? Is there any risk associated with a such mistake except takeoff path looking more like F16 is departing?

If you exceed maximum takeoff/go-around N1 for a given OAT, you are effectively overboosting the engines. The risk is that you are putting more load on the engine components that they are design to withstand.

But is there any way to see that you exceed N1 for a given OAT??? I don't think that N1 gauge is OAT corrected as manual states that 100% corresponds to 7400 RPM.

100% (or whatever the limit is), is rotational limit of the low-speed shaft, it's not a thrust limit. You can only see the latter by inputting the correct temperature into the FMC, which I assume (not familliar with type) calculates the thrust limit on the CRJ.

His question is whether there's an indication that he's put in the wrong temperature, causing the resulting N1 to exceed the thrust limit.

And the answer is no.

But also, the error is opposite of what OP wrote. Inputting a higher temp results in a lower, not higher, N1.

This is not correct. If you input higher temperature RPM will be higher till the flat rate temperature. After flat rate temperature RPM will go down again due to ITT limitation.

I stand corrected, I haven't flown the 200 in a while. In the later models with FADEC, you only input a temperature if you're using flex thrust, and for full thrust you don't do anything and the airplane uses its own temperature sensor in the inlet. So for anything we input, it's only above the flat rate temp. I'd forgotten that in the 200 you input the temp for full thrust too.

Rotor speed gauges will typically only indicate a red line exceedance, not a rating exceedance. Pretty much by definition, hydromechanically controlled engines don't know if they are being overboosted and are only protected against rotor speed and burner pressure red line exceedances.
Any sort of warning that you've exceeded the engine rating on non-FADEC (or a FADEC operating in alternate mode) would need to come from the aircraft side (FMC or similar). Not familar with the CRJ, but on most Boeing models, when operating N1 engines in Alternate mode, there is an EICAS caution message if you exceed the max rated N1 by more than 2% (as calculated by the FMC based on aircraft sensed Total Temp - not any manually input temp).