Homemade pastes... is an individual matter and depends on the variety of things you can find at home.
I have polymethylsiloxane and powders at home - zinc oxide, silicon carbide, silver powder, copper powder, diamond powder and I don`t remember what else.
I could make various pastes, but I don`t because I have no motivation.
Unfortunately, time is not made of rubber and toothpastes are easily available.
I bought one tube of toothpaste and it will probably last me forever.
Something that almost everyone can have at home, at a neighbor`s place or at the nearest gas station is ŁT-43 grease.
Its thermal conductivity is given in various ways - 0.2÷0.3 W/mK.
It is better than air in micro-irregularities and if the radiator surface is flat, it will fulfill its function sufficiently.
If the heat sink and processor are properly fitted, the grease layer may be around 1 µm.
After entering into the formula, it turns out that at a temperature difference of 10 K (10°C), 20 watts of heat will be transferred through one cm² of such a layer.
If the heat sink is not too small, ΔT can be e.g. 50 K and then 100 watts will flow.
ŁT-43 should withstand temperatures and there is no need to replace it.