The power received by an antenna due to thermal radiation is KTB, where K is Boltzmann's constant, T is the antenna noise temperature in K and B is bandwidth in Hz. Since Boltzmann's constant is very small (1.3806503E-23) the power due to thermal noise is received by the antenna is very small.
The antenna noise temperature is the average of the noise temperature of everything the antenna 'sees' weighted by the antenna gain in that direction.
Therefore you want a highly directional antenna so that the antenna beamwidth is completely filled by the person. You also want a wide bandwidth so as to maximise the power received. A dish antenna is therefore probably a good choice.
The temperature of people is about 300K. Assuming an antenna bandwidth of 1 GHz you should get about:
1.38E-23 * 300* 1e9 = 4.14e-12 W = -83.8 dBmYou will not be able to see that on an oscilloscope. To get it up to a detectable level you want a low noise, high gain amplifier after the antenna, then feed the output of the amplifier to a power detector and smooth the output of the power detector with a low pass filter. Now point your antenna at something with a very low noise temperature (the sky is good for this, about 10k) and record the output voltage after the low pass filter. Now point your antenna at a person - you should see a small change in output voltage.
Another problem you have trying to detect thermal radiation from people is that the background also emits thermal radiation, often at a very similar level.
I don't know what that signal you saw on your CRO was, but it doesn't sound like thermal radiation. It could be some sort of interference which is being picked up more efficiently by the antenna.