A desktop computer produces very little in the way of energy output relative to what it consumes. A bit of RF deliberately for Bluetooth and WiFi, a bit of current in Ethernet cables, some RF that is accidental, and some light. Just guessing perhaps a watt or less, if we draw the 'box' around all the peripherals that it is powering such as USB keyboards and such like. So yes, most of the power input ends up as heat.
Aside from the losses in the various power supplies, the chips themselves have a leakage current that is always there (in simple circuits, anyway) and a dynamic current that is caused by the charging and discharging of millions or billions of tiny capacitances within the chips. The faster the nodes change, the higher the voltage change, the larger the capacitances, and the more nodes are changing, the more current and thus the more power. Both of them act as loads on the power supply rails. Most of the power would be dissipated in the transistors (and for the dynamic power during the actual switching), not in on-chip or off-chip wiring. The dynamic power is proportional to the square of the supply voltage.
Each year, the chip features tend to get smaller (so less capacitance per node), the internal core supply voltage lower, and thus the power consumed per calculation tends to drop.