This report from the US Nuclear Regulatory Commission says 141 Ci/g, so 20 g would run
(141 Ci/g)(20 g)($90/0.1 \mathrm{\mu Ci}) = $2.5 trillion. There might be some markup from that vendor.
Thank you for that research. We’re gaining on solving the OP’s problem. 
You’re also paying for a lot of packaging.
You’d have to buy 28,200,000,000 (28 billion) of those little coin thingies to get enough radioactivity, and we know we only need the amount contained in about 5 coin thingies of volume.
This concern might be addressed by dividing a subcritical quantity of U-235 between the cup and its coaster. When the mug is full, the coffee would moderate some fast neutrons back toward the coaster to enhance the reaction. 6 MeV per neutron of thermalization energy would be available to warm the coffee. As the level in the cup drops, there is less moderation and so the reaction slows. When the empty mug is returned to the cupboard, the reaction will be effectively stopped by separating the two half-masses. Bombardment with gammas and neutrons seems a small price to pay for such an elegant solution.
[Moderating]
Since I’ve gotten a number of reports on this thread: Yes, what the OP is asking for is silly. We all know that. But it’s still a factual question. Calling the thread silly, or suggesting more mundane alternatives, are hijacks, and it’s to be expected that the OP would be annoyed by that.
This sounds suspiciously … specific. The “trillions” price tag gives me pause. Darn it.
No, no. Trillions is for strontium. That wasn’t my hare-brained scheme.
There’s 200 MeV of energy to be extracted as heat from each U-235 fission event, so we need about 600 billion fissions per second to produce 18 W. That’s around 15 Ci. The specific activity of U-235 is 2.16\times 10^{-6} Ci/g, so this is sounding like it might be too heavy for a coffee cup. That’s the beauty of using the coffee as a moderator. 4 cm of coffee is sufficient to moderate the neutrons (I’m assuming you’re not drinking heavy coffee) and U-235 has a million times higher capture cross section for thermal neutrons, so we only need about 7 g. Pure U-235 is hard to come by, but natural uranium contains 0.72% by weight of U-235, so we need about a kilogram. That might still seem hefty for a coffee cup but, remember, half of that goes in the coaster. Natural uranium is trading for $60/pound
so I don’t think we’re at an unreasonable price point for coffee that never gets cold.
According to wiki, there are pacemakers with radioactive decay power sources (apparently battery is incorrect terminology), so the OP is not as farfetched I would have assumed.
I think a regular ceramic mug can stand to be heated by 18W continuously. Use a non-heat-conductive material for the handle and exterior base for added comfort.
Back when I used one of those desktop coffee cup heaters I left it on all weekend once or twice, and other than having to clean baked on coffee residue, there wasn’t any damage to the desk or mug.
A friend admired my AC powered one, so he got a USB powered one, and it was worthless. We determined the USB one was .5 watts compared to 18 watts for mine. I’ve long since switched to an insulated mug.
Ooh, ohh. I bow to your superior nuclear-fu!
That is simple, elegant, and self-regulating. The scales have fallen from my eyes. Thank you!
Yeah. I had one that was weight sensitive with a timer, so you neither turned it on, nor could forget to turn it off. My late first wife had a lesser manual version. We She cooked a few 1/4" coffee residues into mud flat over a weekend. Never had a thermally scary outcome, but sometimes the cup interior was pretty scary.
As to USB, one of the coffee warmer examples I saw on Amazon but did not cite was 110V powered, but had a USB-C outlet on it into which you could plug a USB cable to charge your phone or whatever daisy chained off your coffee warmer. Very clever I thought. One can never have too many desktop USB outlets.
0.5W is gimmickry for resistive heating, not a real solution.
Any idea what the critical mass of pure Strontium-90 would be?
I’m not sure it has one. Criticality is not just about the quantity of activity. A critical mass is when every fission induces another fission. I’m not sure that Sr-90 has any significant capture cross section for betas, nor that betas induce fission. Possibly Sr-90 could be surrounded by a reflector that could make more effective use of either betas or the very, very small flux of gammas to generate a flux of something that would induce fission. If you made me guess, though, I’d say no.
IANA nuclear expert. I’m waayy out at the edge my nodding acquaintance level of expertise.
Given that it’s a pure beta emitter, and its daughter product Y-90 is also a pure beta emitter I doubt it has a critical mass; IMO there’s simply not enough energy in each emission to trigger a cascade regardless of beta decay flux density.
As I expect you found, Google & wiki were both uninformative on point.
ChatGPT was no help.
strontium-90 is not fissile
@Napier 's plutonium-238 releases a 5.593 MeV alpha particle per disintegration, with a half life of 87.74 years, which works out to 0.57 watts/gram. So, for 18W, around 46g of the dioxide. Wrap it in a thin little shield and you’re ready to go! Strontium-90 will produce a lot of secondary radiation via bremstrahlung.
I told you the airline cup was here again, Dude.
That doesn’t sound right, because natural uranium isn’t noticeably warm. I think that the specific activity you’re referencing is mostly spontaneous fission, not induced, and so increasing the induced fission by a factor of a million doesn’t increase the total activity rate very much. You’d need a higher density of U-235 atoms (presumably, by using a more concentrated sample) to have much effect.
Have you tried setting a cup of coffee on it?
You’re right that the Oklo reactor is believed to have required the combination of much higher natural concentration of U-235 and the moderating effects of ground water to achieve intermittent criticality. I absolutely made some ridiculous assumptions to get to 18 W, but I wasn’t trying to achieve criticality; just boost sub-critical decay heat. Still, wiki suggests that heavy coffee might be required, after all.
I assume OP meant to say “geothermal is nuclear”.
True, but geothermal relies on the relatively stable temperature of the thermal mass of earth in the first tens of meters below the surface. I’m pretty sure that’s more determined by insolation than it is by decay heat from the core.
Although I guess you could argue that’s ultimately nukular, too.