Reading voltage of an amplified thermopile
You need to ground the negative terminal of the thermopile. 

The LM358 is a single-supply op-amp and it will work with a 5V supply, however the output voltage will be limited to about 0-3V over temperature and a bit more than that typically. 

The LM358 also has a typical offset voltage that can be as much as your entire signal, so it's not a great choice for this application. Ideally get a better op-amp or at least give the op-amp a negative supply and trim the offset out. The sample circuits on the datasheet show a pseudo-ground created by a Zener diode to provide some offset. 

If the particular op-amp sample you have happens to have a large negative offset you'll get about  0V out pretty much regardless of the thermopile output, even when it's connected properly. If it's a positive offset  you'll see a large output voltage (as much as 3V) even without a thermopile signal. 

You should also match the impedances seen by the inputs and add some low pass filtering to an amplifier with such a high gain. For example, a 100nF capacitor across the 1M and another 100nF from the non-inverting input to ground. 

A suitable amplifier would be the NCS325SN2T1G which costs a bit more than an LM358 (32 cents in 100's) but performs much better in this application (low supply current, rail-to-rail input and output, microvolt offset). Don't forget that if you need negative output you need to give it a negative supply (and that particular op-amp can only handle 5.5V so something like -1 + 4V.