My little guy is obsessed with dropping toys behind the radiator....stuff like puzzle pieces, matchbox cars, egg shakers...pretty much anything small-ish. It started out being mildly amusing, but requires the stuff be fetched - a process that involves wedging something narrow back there to get the toy out. (I did it once with a wooden spoon, which has resulted in pretty much all our wooden spoons having spent time behind the radiator!) His fave little figurine, red-haired guy, was just liberated after roughly 3 weeks of heated solitary confinement.
I try to reserve time out for unsafe things (e.g. standing on a chair) or willful disobedience. Would you see the toy in radiator thing as time-out worthy? If not time-outs, how would you curb it?
I'm strict in some ways (food choices, screentime, no hitting, no throwing toys, firm bedtime), but I'm pretty chill about others. I'm fine with LO helping me dump coffee beans in the grinder, even if that means 5 minutes of sweeping when 1/3 fall on the floor. I'm cool with him building a tower of empty clean recyclables while I make dinner. I'll let him help put his clothes in his dresser, even if it means some stuff gets rumpled. But this probably crosses the line.

Re: Reining in Cantankerousness
This will only work if he's bothered that things go missing.
The other thought I had is there any way you can close off some of the access so it's less appealing? We have acking tape over the hole in our subwoofer to prevent B from shoving thingds in there.
BFP #2 5/27/12. EDD 2/1/13. m/c and D&C 6/21/12.
For us, in cases like that, it's the object that goes in time out, not the kid. Similar to what PP said - I'll get the toy out once, but if you do it again, then you don't get it back.
Just one example - DS loves putting his big firetruck on the coffee table, but then it rolls off very easily & it slams down on the hardwood floor. The rule is that the firetruck stays on the floor & is not to be put on the table. If I see it on the table, I ask him nicely to put it down on the floor. If he doesn't listen & it inevitably falls on the floor, the firetruck gets put on time out.
He gets more enjoyment from dropping the toys, I think, than the toys themselves. (Red-haired guy was the exception). So I'm not sure whether toy timeouts would work...but that may be our best option.
We have a friend who wants to start a radiator cover business! But ours don't get too hot and since we have a gazillion other home improvement projects that are more urgent, I think it will be a while before we get them.