Yes it's theoretically possible that we could do enough nuclear fission to raise the global heat content of the earth significantly. But in reality, we've done very little nuclear fission industrially, and it's a tiny tiny contribution.
First, remember that burning fossil fuels also adds to the global heat content. And that way way outstrips nuclear fission: each year, nuclear contributes to about 6% of global energy demand. That's less than we get from renewables, and much much less than we get from natural gas, coal and oil (those last three total around 80% of the global energy supply). So the contribution to the global heat content from nuclear is smaller than that from fossil fuels. All in all, the combined output from nuclear, oil, gas and coal is the equivalent of about 12TW of extra heat into the Earth (in mean power terms).
But that's tiny compared to the impact on global heat content from anthropogenic greenhouse gases.
The Earth's surface is around $5\times 10^{14} m^2$, so 12TW is about $0.025W / m^2$. The radiative forcing from $CO_2$ is around $1.8W / m^2$
Increasing the atmospheric concentrations of greenhouse gases directly (in particular, $CO_2$, but also $CH_4$ and several others), and indirectly, through secondary feedbacks and forcings, causes an increase in global heat content that is orders of magnitude larger than the heat added to the Earth from all human activities.