I currently have a Honeywell T451A thermostat and would like to replace it with a programmable one.
It controls the downstairs heating zone of hot-water baseboard heaters. The heat comes from an oil furnace. There are only two heavy wires used to connect the thermostat.

I am confused about why I cannot use just any Line Voltage programmable thermostat.
Just queried Honeywll about their Aube TH106 240V Thermostat, which is listed as being for 2 wire SPST, and a capacity of 2000 watts @ 120V. But the techie told me that this particular one would not handle the "load".
Can anyone help me to understand just what I am seeking in way of a replacement, based on the fact that I had a T451A thermostat previously? Am not necessarily looking for particular brands or items, just the “requirements” that I must seek.
Thanks in advance for your help.

First you need to know the exact load your system will put on the thermostat.

You will have to use a watt meter and jump the bare wires at the thermostat to judge the load.

Without that info it will be hard to pick a thermostat of any kind sinve they are all load rated.

There are many brands and models available but you have to know the basics first.

Usually when you see to heavy wires that means that the thermostat has to be able to carry a good sized load.

Can the measurement of watts, referenced in the prior answer, be attained using an OHM meter? Or do I need a different instrument?

A ohm meter will not work.

To read true watts you need a watt meter

OR a Amprobe for amps then do a amps to watts conversion.

All HVAC service people have these meters on the truck. This is one reason service calls are so expensive. You need $$$$$$$$$ worth of tools just to be able to work in the trade.

Neat trick: amps to Watts? W=(Amps)(Volts) most of the time.

It is such a imperfect world we live in.LOL

Yep. For those that know when to use W=VI and when not to: https://www.ohiosemitronics.com/pdf/tech_papers/Harmonic%20distortion(A).pdf

I do have a true RMS meter. Expensive when I bought it years ago before they were popular and cheap. Back in the day when they called variable speed motors ICM's (Intergrated Control Motors) I needed it for accurate testing purposes in today's world the same motor is called a ECM (Electronically Commutated Motor).

It is a mandatory class tool but if no money exists for them to purchase and bring to class I let them use mine. Since I try to help the guys in class learn what quality is Fluke supplys me with all there meters for free. Right now I am using a 289/FVF data logging. I had the 87 V but I like the features of the 289 better. It is a great toy as I call all my tools.

The other end of the spectrum is covered by SPX Service Solutions (Robinair)
SPX TIF Corporation
Amprobe and UEI

UEI sends a few of there cheaper China made meters for use in class. When class is over I usually pick the ones in class with a serious lack of funds condition and give them one of the meters. UEI blesses this give away and it is good advertising for them so when the guys start to make some $$$ they will be loyal for awhile and buy there equipment.

Lucky. It's hard enough explaining to someone why you need to measure TRMS.