You don't know what you're talking about. Copper is very conductive compared to solder.
Pure copper has a resistivity of 0.0172µΩ⋅m while 63% tin/37% lead solder has a resistivity of 0.145µΩ⋅m. (http://alasir.com/reference/solder_alloys/) That's almost an order of magnitude difference.
Let's say you had the absurd case of 1/2 copper and 1/2 solder. I = I_cu + I_solder, and V = I_cu * R_cu = I_solder * R_solder => 8x more current going through the copper than the solder.
You would need 8x more solder than copper in order to get "more current going through the solder than the actual wire."
Well hey, I guess I hit it on the head with them being at least within an order of magnitude, eh?
You forgot to take into consideration the thermal conductivity of solder. Although there's only 1/8th the current going through the solder than that of the wire, solder has a much much lower thermal conductivity than copper. After a bit of googling, copper's thermal conductivity is 401W/(mK) and bismuth solder is 19W/(mK). Although there's less current going through that solder, it's so much more thermally conductive it'll probably see its temperature increasing faster than that of the copper.
That certainly doesn't help when solder's melting point tends to be around 140C and copper's is 1000C. Also, while you may have said a 50/50 mix of solder and copper is extreme, if the OP was an awful at soldering and was using something like 16 gauge wire, it's not so ridiculous that there may be a 50/50 mix of solder to wire, hell that might even be a bit low.
The numbers you yourself reported show that copper is much more thermally conductive than solder, and not the other way around.
Thermal conductivity describes how quickly the heat conducts through the wire. Since the wire is uniformly heated, this is a minor detail (assuming that the wire's thermal conductivity is considerably higher than the electrical insulation around the wire). Instead, you need to look for the heat transfer coefficient of insulated wire.
The melting point of Sn63Pb37 is 183C, not 140C. 183 is not "around 140."
If the wire were hot enough to melt the solder in a copper+solder combination then it would be well more than hot enough to melt the plastic insulation around just the copper wire itself, which is typically rated for only 90C.
Pure copper has a resistivity of 0.0172µΩ⋅m while 63% tin/37% lead solder has a resistivity of 0.145µΩ⋅m. (http://alasir.com/reference/solder_alloys/) That's almost an order of magnitude difference.
Let's say you had the absurd case of 1/2 copper and 1/2 solder. I = I_cu + I_solder, and V = I_cu * R_cu = I_solder * R_solder => 8x more current going through the copper than the solder.
You would need 8x more solder than copper in order to get "more current going through the solder than the actual wire."