There are Some on my Website as Projects and have some Kits Available.
But I Don't actually build them as a Finished Product.
If you buy One, It needs to be made for 12 Volts and capable of delivering the required Current to your Nichrome wire.
Curious, What kind of Silicone are you using to...
The Temperature of the Wire is Not so Important.
You can determine the Current you want to supply and than determine the Length of wire needed for this current.
Than you need to put the Nichrome Wire around the filter and Insulation around the whole thing.
You also need get or make a Sensor to...
Many of them, But the largest I built was 100 Watts per channel.
Universal Tiger Amp, from Popular Electronics, Many Years Ago.
Shakes my Living Room Pretty Good.
What are you intending to use as a Power Source for this?
Battery or power adapter.
That Module is 3.8 volts, somewhat an odd rating for either of these sources..
Want to talk, the UK is a free phone call for me.
For Better Explanations.
For Constant Temperature, Would require a Temperature Monitoring Probe and Current Control Circuits.
NOT EASY with your Proposed Push Button Control.
What is your Power Source?
Why such a Low Voltage Peltier?
3.8 Volts?
All the ones I use are rated nominal 14.4 volts.
As needed for Automotive applications.
Heating verses cooling, Just reverse the polarity.
But what is your application?
Yes regulating the Temperature is Good, Especially Important on the HOT Side.
Yes that will work, But Depending on the Value of the Sensing Resistor "RS", You get a Voltage Drop.
This is Basically the Same as what "BobK" Said.
And with your Power Supply, there are No Other Options.
Well if you Can't read the Numbers, STOP THERE.
Just because parts look the same, Does NOT mean they are.
And I have some NEW Parts, that are Difficult to read the Numbers on them,
They DON'T Look Bad in your Picture.
Since you Don't know the Exact Specifications of the Original MOSFET's, Your just Compounding the problem of obtaining a Correct Repair.
YOU CAN'T TEST THESE MOSFETS "IN CIRCUIT" like that.
That would be a Test from "Gate to Source" and your actually reading the Resistance of Other Parts on the Circuit Board.
A Diode Test will test a MOSFET for Drain to Source.
Should read Infinity in one direction, and around 0.5 in the other direction.
But not the Gate function.
And the MOSFET MUST BE REMOVED FROM THE PCB For This Test.
MOST MOSFET's have Copper Leads and Tabs. They are Tinned but Never Seen one with RUST.
There is usually a Silicon based Thermal Grease put on the MOSFET to help HEAT CONDUCTION between the MOSFET and the Heat Sink.
There is NOTHING Inside the MOSFET that can LEAK.
How were you Measuring this...