I have 2 boilers in my house. 1 is for the main house and the other one is for the annex which is built a few feet away from the main house. My 1st boiler is connected to Nest thermostat. Can I connect my 2nd boiler to the same Nest thermostat?
If the tstats get power from the boilers, the OP would have to be sure than only one of the boilers is supplying power to the Nest tstat. If the transformers were out of phase, you'd have a direct short. A dry contact relay for the 2nd boiler control would be safer, triggered by the call for heat on the first boiler.
But clearly the OP has 2 zones and 2 tstats are called for...best and safest approach. Like Freeman said, unless the heating performance and heat loss of the two spaces are identical, one space will be either over-heated or under-heated compared to the other.
BTW, what is currently controlling the 2nd boiler? A tstat in the outbuilding? An old fashioned manual one? If so, I really think the best solution would be to replace it. It doesn't need to be a super expensive Nest type...programmable tstats for heating only shouldn't cost much more that $50-$60. Probably the best and least expensive solution.
I'm sure it would be a simple matter to run the wires from one thermostat to two different boilers in the two buildings, but you would have only one set point for both of them.
Which ever one the thermostat is in (the "main" building) would be heated to the proper set point, the other (the "secondary" building) would be heated for the same amount of time that it takes to keep the main building at the proper temperature, but not necessarily to the desired temperature.
For example, lets say it takes 30 minutes out of each hour to keep the main building at the desired temperature.
- The secondary building may be over heated when the heat runs for the 30 minutes necessary for the main building.
- The secondary building may be also be under heated with the heat only running for those 30 minutes.
It all depends on how accurately sized the heaters are for their respective buildings and whether they, and the heat distribution (forced hot air? heated floors? radiators? other?) systems, run at the same rate and efficiency.