I want to estimate the total noise(all sources) at the output terminal of a transimpedance amplifier (AD8009). Is it the input current noise times the transresistance or does one need to add the thermal noise ((4*Kb*T*R)^1/2) separately to get the total noise?

You need to add all the noise sources together in a consistent manner. Assuming they are uncorrelated, they all add as the square root of the sum of the squares. I usually tackle transimpedance amplifier by converting all noise sources into currents at the inverting inputs. The sources are therefore:

1. Amplifier current noise at the non-inverting input.

2. Feedback resistor thermal noise.

3. Amplifier voltage noise divided by the impedance to ground at the non-inverting input (N.B. this is the feedback impedance in parallel with the source impedance)

4. Source noise as a current (ignore this if you just want the amplifier contribution)

Once you have all these current noise sources summed, you can get the output voltage noise by multiplying by the feedback impedance.

This approach works best for noise density, which you can integrate over your bandwidth to get total noise.

It's important to include source and feedback capacitance in your impedances as these can easily dominate the result.