Mmm.. some brute force going on there.
See for example,
etc. etc. There are literally dozens of these things, possibly over a hundred on the market currently. I've got at least one kicking around here.
I designed one (mumble) years ago, but it was never built (looked good on paper, I have no doubt it would have met specifications). Really all you do is measure excitation current and source a precise voltage appropriate to the simulated resistance (one multiplication). The rest is all details.
Tens of milliseconds or slower. You need a lot of low-pass filtering (and preferably measured over an integral multiple of power line frequency) in a typical industrial system so I think you can count on it not being really fast for most general-purpose applications. The kind that's integrated with the sensor in one package could be much faster, but I don't see why anyone would would be fool enough to design it that way (famous last words?). Temperature generally changes slowly and RTDs are generally a relatively slow sensor.
Best regards, Spehro Pefhany